text:
User talk:Shimmin

Hello from Mav149
Hello and Welcome! Great work on Thorne-Zytkow object! --mav

Names of People
Please see my comments on Talk:Sharaku about your name change; see also Naming conventions (common names) and Naming conventions (use English). for the standard Wiki policy on names. Noel 04:33, 20 Aug 2003 (UTC)

PS: By the way, I actually agree with you that it would preferable to file articles for people under their full names, with redirects from "common" names to the article. Alas, that's not the policy on the Wikipedia (as I found out painfully when I tried to reorganize the Medici pages into rational order). So now I dutifully file articles under the most common form of the name, even when I really don't like it (e.g. see my comments on the Talk:Toyokuni page. Noel 16:17, 20 Aug 2003 (UTC)

Names of Chemicals
I've been away for a few days, just seen your message. My recollection is that the convention is to use the IUPAC name unless there the substance is almost invariably known by the common name (like water) - can't rember where it says that though. jimfbleak 15:08, 24 Aug 2003 (UTC)

Names of Schismatic Religious Institutions
Hi there. Just a short note to say that your change of true Catholic Church to True Catholic Church was incorrect and I have changed it back. It deliberately lowercases the word true in its name. The first letter of a link is not case specific, though unfortunately in the actual title is automatically begun on our pages with in upper case, which causes problems for things like iMac, eMac, tCC, etc that use the lowercase. But the text of the article on the tCC makes it clear that the word true in the church name is lowercase. FearÉIREANN 20:52, 24 Aug 2003 (UTC)

Complaint about Death in Canada
Hello, why did you delete the stuff realted to Canada in the death aticle? Also why did you mark that change as a minor edit? - SimonP 22:14, Aug 26, 2003 (UTC)

Multics and ASCII-1963
Your recent edit of new line does not match with my recollection of what Jerry Saltzer (who designed the Multics I/O system) told me. (However, my archives only contained my half of the conversation so I don't have a direct record of what he actually said.) He briefly described the process of converting all of the Multics source code from 1963 to 1968 ASCII (which was stored on the Project MAC CTSS system, which used a different coding system, because they didn't have the GE 645 hardware yet) and having to redo all of the compilers and other text-processing utilities to know the new code for line termination. I suspect you could find details of this in old Project MAC technical reports. If I remember, I can ask Jerry or Corby next time I see one of them. 18.24.0.120 05:28, 19 Feb 2004 (UTC)

While I certainly defer to your source's knowledge of Multics, the story does not jibe with published standard for ASCII-1963, which does not contain a separate codepoint for newline.

In 1963 ISO's draft standard said:

The controls CR and LF are intended for printer equipment which requires separate combinations to return the carriage and feed a line.

As an alternative, for equipment which uses a single combination for a combined carriage-return and line-feed operation (called New-Line), NL will be coded at F 2 or FE 2 [i.e., 6-bit 0/2 or 7-bit 0/10, LF]. Then F 5 [6-bit 0/5, CR] will be regarded as a Spare Control, and FE 5 [7-bit 0/13, CR] will be regarded as Backspace BS.

If the latter type of equipment has to inter-work with the former, it may be necessary to take steps to introduce the CR character.

But ASA's standard made no such provision. In 1967 John Booth (who was AT&T's representative on the ASCII committee, and so may have known about Multics) proposed that LF as NL be allowed in the American standard, but he only got the following compromise language which appeared for the first time in USASI's 1968 standard:

Where appropriate, this character may also have the meaning "New Line" (NL), a format effector which controls the movement of the printing position to the first printing position on the next printing line. Use of this convention requires agreement between sender and recipient of data.

Booth tried again in 1972 to make 0x0a primarily a newline character, rather than a codepoint that could be used as a newline with prior agreement bewteen parties, but this change, while existing in some drafts for a revised ASCII, did not make it into the 1977 standard.

So basically, there never was a standalone newline character in any version of ASCII, and LF is the only character with even approximately this meaning.

Since your source worked on I/O code, perhaps his complaints related to EBCDIC, which Multics would have had to convert to if it wished to output to an IBM peripheral. Many versions of EBCDIC do contain all of CR, LF, and NL.

 * Thanks for the details. Hopefully next time I run into Jerry and/or Corby I can put this question to them directly.  18.24.0.120 06:22, 22 Feb 2004 (UTC)

Galileo and the telescope
If he did not invent it, who did? He certainly improved the quality of the instrument (he learnt lens-grinding painstakingly to do so), and was the the first to point it skyward. Lenses were "invented" in Holland, that much I know...

Urhixidur 01:33, 2004 Jul 29 (UTC)

 * The telescope was invented in the Dutch Republic, probably in late August or early September of 1608. No one knows who exactly deserves credit.  A Dutch newspaper briefly mentions the new device being shown off to visiting dignitaries on 10 September 1608, and in the last week of September, three different lensmakers all applied to the Dutch government for patents on the device.  Hans Lippershey's application made it in first.  None of the patents were granted.  Also in the last week of September 1608, a telescope was for sale in Frankfurt.  Galileo heard about the instrument through diplomatic correspondence, and from the descripton given, set about constructing his own instruments sometime early in 1609.  By the fall of that year, he had built a 10x instrument, which was almost certainly the most powerful in the world at the time.

 * As for being the first to point it skyward, sorry again. It's simply a natural thing to do if you have one, and that same 10 September 1608 news report lists the skies as among the objects viewed by those first known telescope users.  In June 1609, Thomas Harriot made a sketch of the moon as seen through a 3-power scope, and Galileo did not make any record of his lunar observations until October.

 * By fall of 1609, Galileo did have the best telescopes in the world, and his Siderius Nuncius (March 1610) was the first scientific treatise based on telescopic observations, but the evidence simply does not support crediting him with either inventing the telescope or making the first telescopic astronomical observations.

Please add licence information by the picture Image:Formic-acid.png.Thanks.--Van Flamm 14:39, 6 Sep 2004 (UTC)

beta Systemic Bias section
Hi, if you wish to help contribute to a beta version of a Wikipedia page section designed to counter-act Wikipedia's systemic bias, please sign the bottom of this section on the Village pump - Village_pump. If not, no worries.--Xed 03:52, 22 Sep 2004 (UTC)

Article Licensing
Hi, I've started a drive to get users to multi-license all of their contributions that they've made to either (1) all U.S. state, county, and city articles or (2) all articles, using the Creative Commons Attribution-Share Alike (CC-by-sa) v1.0 and v2.0 Licenses or into the public domain if they prefer. The CC-by-sa license is a true free documentation license that is similar to Wikipedia's license, the GFDL, but it allows other projects, such as WikiTravel, to use our articles. Since you are among the top 2000 Wikipedians by edits, I was wondering if you would be willing to multi-license all of your contributions or at minimum those on the geographic articles. Over 90% of people asked have agreed. For More Information:
 * Multi-Licensing FAQ - Lots of questions answered
 * Multi-Licensing Guide
 * Free the Rambot Articles Project

To allow us to track those users who muli-license their contributions, many users copy and paste the " " template into their user page, but there are other options at Template messages/User namespace. The following examples could also copied and pasted into your user page:

 * Option 1
 * I agree to multi-license all my contributions, with the exception of my user pages, as described below:

OR
 * Option 2
 * I agree to multi-license all my contributions to any U.S. state, county, or city article as described below:

Or if you wanted to place your work into the public domain, you could replace " " with "  ". If you only prefer using the GFDL, I would like to know that too. Please let me know what you think at my talk page. It's important to know either way so no one keeps asking. -- Ram-Man (comment| talk)

Pudding/puddling
I've reverted your change to Pudding furnace for the moment while I do some research. On first glance, your change may seem correct, but Google seems to say otherwise (unless they are all mirrors of Wikipedia). I'll do some research to see if one outweighs the other, and if there is appropriate etymology. Noisy | Talk 22:08, Feb 10, 2005 (UTC)

Vote on Talk:Gdansk/Vote
Hi. Since you have edited on pages with disputes about the names of Polish/German locations, I would invite you to vote on Talk:Gdansk/Vote to settle the multi-year dozens-of-pages dispute about the naming of Gdansk/Danzig and other locations. The vote has two parts, one with questions when to use Gdansk/Danzig, and a second part affecting articles related to locations with Polish/German history in general. An enforcement is also voted on. The vote has a total of 10 questions to vote on, and ends in two weeks on Friday, March 4 0:00. Thank you -- Chris 73 Talk 00:42, Feb 18, 2005 (UTC)

Muhammad/Mohammed/etc.
Hi. My intent wasn't to annoy others (and I certainly hope that hasn't happened), but while I can see that making substantive posts to wikipedia is perhaps a better use of time than standardizing spelling, I still feel that a name should not be spelled 9 different ways across Wikipedia (Muhammad, Mohammed, Mohammad, Muhammed, Mohamed, Muhamad, Muhamed, Mohemed, Mahomet). Within some individual articles, 2 or even 3 different spellings were used. The easiest way to fix this, in my opinion, was to simply change all of these spellings to Muhammad. I believe that many of the misspellings were typos, and others were due to articles being from the 1911 Brittanica, etc. I don't really see any harms associated with a standardized spelling. So I'm sorry again if I angered anyone. Hopefully consistency will help Wikipedia more than hurt it.

--Jacobolus 20:28, 5 Mar 2005 (UTC)

User:Jcbos and "Christian Bible"
User:Jcbos has started another vote on the "Christian Bible" issue, at Talk:Bible. Thought you'd want to know. Jayjg (talk) 18:34, 17 Mar 2005 (UTC)

Very good

 * I have never before heard used "left behind" as a euphemism for "beheaded."

Just a quick note to say thank you for making me chortle! Cheers --Etimbo | Talk 12:38, 18 Mar 2005 (UTC)

Fiction guidelines
Hi there! Just wanted to say that your guideline for characters from fiction is brilliant. I've added it as a guideline at WP:FICT and hope it gets used a lot! Radiant_* 12:36, Mar 29, 2005 (UTC)

Prophecy of the Popes
Hi!

Why did you remove the part that refers to the history of the article as an example of postdiction in Prophecy of the Popes (Talk:Prophecy of the Popes)? I think it was perfectly appropriate. Is there a Wikipedia policy not to do self-references?

Thanks,

UnHoly 01:09, 20 Apr 2005 (UTC)

 * Yes, according to semi-policy, self-reference is poor form. Please see WP:ASR. Shimmin 01:34, Apr 20, 2005 (UTC)

 * Ok, thanks. I tried a rewrite. UnHoly 14:47, 20 Apr 2005 (UTC)

Comet references
Thank you very much for your efforts. It's been an uphill battle to spread the word about how important citing sources and verifiability is, but we're getting there. What you've done is great, and keep it up. The thing I like better about the Footnotes3 autonumbering method is that it creates a link down to the notes section and back. But any inline citation method is better than none. Also ideally all the inline external links should be collated as references at the bottom, formatted as at Cite sources, and cited in a consistent manner with other citations. Thanks again - Taxman 15:53, Apr 25, 2005 (UTC)

Naming conventions (chemistry)
Thank you for contributing to Naming conventions (chemistry). I have now summarized the discussion on that page and added certain points which have been discussed at WikiProject Chemicals. Any comments, and especially improvements, on the results would be more than welcome. Physchim62 7 July 2005 11:03 (UTC)

Image deletion
Listed under Images and media for deletion/2005 September 12. Thunderbrand 21:05, September 12, 2005 (UTC)

Spelling
Please don't change american spellings to british spellings. Unless its a british topic, articles which start as american spelling stay that way (same for articles that start as british spelling). See WP:MOS --Duk 14:05, 15 October 2005 (UTC)
 * Oops, sorry. --Duk 15:56, 15 October 2005 (UTC)

Citation issues
You may be interested in reference/citation content/format issues in Talk:Global cooling (see preceding discussion) and Requests for comment/SEWilco. (SEWilco 05:54, 30 November 2005 (UTC))

Babel
Could you consider adding this template to your userpage? It is very helpful in case translators are needed and such.--Piotr Konieczny aka Prokonsul Piotrus Talk 15:30, 9 December 2005 (UTC)

Sources for Prout's hypothesis
Hello, some time ago you added a fair bit of content to Prout's hypothesis. As you may be aware, we are currently trying to improve Wikipedia's verifiability and reliability by making sure articles cite the sources used to create them. Do you remember what websites, books, or other sources you used to add content to Prout's hypothesis? Would it be possible for you to mention them in the article? See WP:CITET for some quick templates to use for citing sources. Thanks! --best, kevin [kzollman][talk] 02:23, 10 December 2005 (UTC)

Glucose
Do you think User:BorisTM is unreasonable on the Glu/Glucose issue? GraemeLeggett 16:06, 17 January 2006 (UTC)

Yes. Looking at his contributions and talk page, he does appear to be acting in good faith, but his behavior in this instance seems to me an unreasonable pursuit of poor prose. Shimmin 18:00, 17 January 2006 (UTC)

North American area codes
Uncle G's major work 'bot is about to move another ... er ... small hill. But a consensus is required on the naming scheme to be employed. Please review Category:Greek Area Codes, Category:United Kingdom area codes, and Category:North American area codes, and then contribute to the discussion at Talk:North American Numbering Plan. Uncle G 21:11, 19 January 2006 (UTC)

License tagging for Image:Ctk-1-phenylethanol.png
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Image Tagging for Image:Ctk-arrow-right.png
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Image Tagging for Image:Ctk-minus.png
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Silane
Thanks for the Silane article improvement a while back. Do appreciate it. Do you buy the "Silicon Based Life Forms" Theory or is that SILI? Mike Hooten Concord, NC mlhooten(at)gmail.com michael.hooten.name

Trichloroethylene
In the article Trichloroethylene you created in August 2003, you note that TCE is insoluble in water. I thought it was quite soluble. Do you have a reference? Nfitz 20:37, 8 September 2006 (UTC)

 * I probably got that from the uakron database: . However, the version of that page presently linked from the article  gives a solubility of 1 g/L in water. Shimmin 22:59, 8 September 2006 (UTC)
 * Shouldn't TCE provide reference temperature ... and an actual reference for the information? Nfitz 06:52, 9 September 2006 (UTC)

Iron and steel
I note that you have amended the hisotrical section of the article on steel in the past. I have merged with with a similar section in Iron to form a new History of Ferrous Metallurgy. In editing the prehistoric part of this, I have been working outside my area of expertise. If you know about this, could you look at and correct the article? Peterkingiron 00:07, 18 December 2006 (UTC)

request to move to kyiv
Hello,

I have set up a request to move the page Kiev to Kyiv.

I have outlined four key reasons for doing so in the discussion section of the page.

Looking through the archives, I saw that you had contributed to this page earlier. I would like to hear what you have to say on this topic.

Thank you

Horlo 02:51, 30 July 2007 (UTC)Horlo

Image:Formaldehyde.png listed for deletion
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Image:Propionic-acid.png listed for deletion
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File source problem with File:Mauveine-A.PNG
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Nomination for deletion of Template:Hnote
Template:Hnote has been nominated for deletion. You are invited to comment on the discussion at the template's entry on the Templates for discussion page. Thank you. -— Gadget850 (Ed)  talk 19:58, 13 June 2010 (UTC)

File source problem with File:Test-benzene.png
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File:Test-cyclohexane.png missing description details
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File:Ctk-plus.png missing description details
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File source problem with File:Ctk-plus.png
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File:Ctk-ethylbenzene.png missing description details
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Proposed Image Deletion
A deletion discussion has just been created at Category talk:Unclassified Chemical Structures, which may involve one or more orphaned chemical structures, that has you user name in the upload history. Please feel free to add your comments.  Ron h jones (Talk) 23:06, 10 June 2011 (UTC)

File:Test-cyclohexanone.png needs authorship information.
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File:Test-cyclohexanol.png needs authorship information.
Dear uploader:

The media file you uploaded as File:Test-cyclohexanol.png appears to be missing information as to its authorship (and or source), or if you did provide such information, it is confusing for others trying to make use of the image.

It would be appreciated if you would consider updating the file description page, to make the authorship of the media clearer.

Although some images may not need author information in obvious cases, (such where an applicable source is provided),authorship information aids users of the image, and helps ensure that appropriate credit is given (a requirement of some licenses).

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title: User talk:Shimmin


text:
Transpose

In linear algebra, the transpose of a matrix is an operator which flips a matrix over its diagonal; that is, it switches the row and column indices of the matrix $A$ by producing another matrix, often denoted by $A^{T}$ (among other notations).

The transpose of a matrix was introduced in 1858 by the British mathematician Arthur Cayley. In the case of a logical matrix representing a binary relation R, the transpose corresponds to the converse relation RT.

Definition
The transpose of a matrix $A$, denoted by $A^{T}$, $⊤A$, $A⊤$, $$A^{\intercal}$$, $A′$, $A^{tr}$, $^{t}A$ or $A^{t}$, may be constructed by any one of the following methods:
 * 1) Reflect $A$ over its main diagonal (which runs from top-left to bottom-right) to obtain $A^{T}$
 * 2) Write the rows of $A$ as the columns of $A^{T}$
 * 3) Write the columns of $A$ as the rows of $A^{T}$

Formally, the $i$-th row, $j$-th column element of $A^{T}$ is the $j$-th row, $i$-th column element of $A$:

 * $$\left[\mathbf{A}^\operatorname{T}\right]_{ij} = \left[\mathbf{A}\right]_{ji}.$$

If $A$ is an $m × n$ matrix, then $A^{T}$ is an $n × m$ matrix.

In the case of square matrices, $A^{T}$ may also denote the $T$th power of the matrix $A$. For avoiding a possible confusion, many authors use left upperscripts, that is, they denote the transpose as $^{T}A$. An advantage of this notation is that no parentheses are needed when exponents are involved: as $(TA)n = T(An)$, notation $TAn$ is not ambiguous.

In this article this confusion is avoided by never using the symbol $T$ as a variable name.

Matrix definitions involving transposition
A square matrix whose transpose is equal to itself is called a symmetric matrix; that is, $A$ is symmetric if
 * $$\mathbf{A}^{\operatorname{T}} = \mathbf{A}.$$

A square matrix whose transpose is equal to its negative is called a skew-symmetric matrix; that is, $A$ is skew-symmetric if
 * $$\mathbf{A}^{\operatorname{T}} = -\mathbf{A}.$$

A square complex matrix whose transpose is equal to the matrix with every entry replaced by its complex conjugate (denoted here with an overline) is called a Hermitian matrix (equivalent to the matrix being equal to its conjugate transpose); that is, $A$ is Hermitian if
 * $$\mathbf{A}^{\operatorname{T}} = \overline{\mathbf{A}}.$$

A square complex matrix whose transpose is equal to the negation of its complex conjugate is called a skew-Hermitian matrix; that is, $A$ is skew-Hermitian if
 * $$\mathbf{A}^{\operatorname{T}} = -\overline{\mathbf{A}}.$$

A square matrix whose transpose is equal to its inverse is called an orthogonal matrix; that is, $A$ is orthogonal if
 * $$\mathbf{A}^{\operatorname{T}} = \mathbf{A}^{-1}.$$

A square complex matrix whose transpose is equal to its conjugate inverse is called a unitary matrix; that is, $A$ is unitary if
 * $$\mathbf{A}^{\operatorname{T}} = \overline{\mathbf{A}^{-1}}.$$

Examples
1 & 2 \end{bmatrix}^{\operatorname{T}} = \, \begin{bmatrix} 1  \\    2  \end{bmatrix} $$
 * $$\begin{bmatrix}

\begin{bmatrix} 1 & 2 \\    3 & 4  \end{bmatrix}^{\operatorname{T}} = \begin{bmatrix} 1 & 3 \\    2 & 4  \end{bmatrix} $$

\begin{bmatrix} 1 & 2 \\   3 & 4 \\    5 & 6  \end{bmatrix}^{\operatorname{T}} = \begin{bmatrix} 1 & 3 & 5\\    2 & 4 & 6  \end{bmatrix} $$

Properties
Let $A$ and $B$ be matrices and $c$ be a scalar.

 * $$\left(\mathbf{A}^\operatorname{T} \right)^\operatorname{T} = \mathbf{A}.$$
 * The operation of taking the transpose is an involution (self-inverse).
 * $$\left(\mathbf{A} + \mathbf{B}\right)^\operatorname{T} = \mathbf{A}^\operatorname{T} + \mathbf{B}^\operatorname{T}.$$
 * The transpose respects addition.
 * $$\left(c \mathbf{A}\right)^\operatorname{T} = c \mathbf{A}^\operatorname{T}.$$
 * The transpose of a scalar is the same scalar. Together with the preceding property, this implies that the transpose is a linear map from the space of $m × n$ matrices to the space of the $n × m$ matrices.
 * $$\left(\mathbf{A B}\right)^\operatorname{T} = \mathbf{B}^\operatorname{T} \mathbf{A}^\operatorname{T}.$$
 * The order of the factors reverses. By induction, this result extends to the general case of multiple matrices, so
 * $$\det \left(\mathbf{A}^\operatorname{T}\right) = \det(\mathbf{A}).$$
 * The determinant of a square matrix is the same as the determinant of its transpose.
 * The dot product of two column vectors $(A_{1}A_{2}...A_{k−1}A_{k})^{T} = A_{k}^{T}A_{k−1}^{T}…A_{2}^{T}A_{1}^{T}$ and $a$ can be computed as the single entry of the matrix product$$\mathbf{a} \cdot \mathbf{b} = \mathbf{a}^{\operatorname{T}} \mathbf{b}.$$
 * If $b$ has only real entries, then $A$ is a positive-semidefinite matrix.
 * $$ \left(\mathbf{A}^\operatorname{T} \right)^{-1} = \left(\mathbf{A}^{-1} \right)^\operatorname{T}.$$
 * The transpose of an invertible matrix is also invertible, and its inverse is the transpose of the inverse of the original matrix. The notation $A^{T}A$ is sometimes used to represent either of these equivalent expressions.
 * If $A^{−T}$ is a square matrix, then its eigenvalues are equal to the eigenvalues of its transpose, since they share the same characteristic polynomial.
 * Over any field $$k$$, a square matrix $$\mathbf{A}$$ is similar to $$\mathbf{A}^\operatorname{T}$$.
 * This implies that $$\mathbf{A}$$ and $$\mathbf{A}^\operatorname{T}$$ have the same invariant factors, which implies they share the same minimal polynomial, characteristic polynomial, and eigenvalues, among other properties.
 * A proof of this property uses the following two observations.
 * Let $$\mathbf{A}$$ and $$\mathbf{B}$$ be $$n\times n$$ matrices over some base field $$k$$ and let $$L$$ be a field extension of $$k$$. If $$\mathbf{A}$$ and $$\mathbf{B}$$ are similar as matrices over $$L$$, then they are similar over $$k$$. In particular this applies when $$L$$ is the algebraic closure of $$k$$.
 * If $$\mathbf{A}$$ is a matrix over an algebraically closed field in Jordan normal form with respect to some basis, then $$\mathbf{A}$$ is similar to $$\mathbf{A}^\operatorname{T}$$. This further reduces to proving the same fact when $$\mathbf{A}$$ is a single Jordan block, which is a straightforward exercise.
 * If $$\mathbf{A}$$ is a matrix over an algebraically closed field in Jordan normal form with respect to some basis, then $$\mathbf{A}$$ is similar to $$\mathbf{A}^\operatorname{T}$$. This further reduces to proving the same fact when $$\mathbf{A}$$ is a single Jordan block, which is a straightforward exercise.

Products
If $A$ is an $A$ matrix and $m × n$ is its transpose, then the result of matrix multiplication with these two matrices gives two square matrices: $A^{T}$ is $A A^{T}$ and $m × m$ is $A^{T} A$. Furthermore, these products are symmetric matrices. Indeed, the matrix product $n × n$ has entries that are the inner product of a row of $A A^{T}$ with a column of $A$. But the columns of $A^{T}$ are the rows of $A^{T}$, so the entry corresponds to the inner product of two rows of $A$. If $p_{i j}$ is the entry of the product, it is obtained from rows $i$ and $j$ in $A$. The entry $p_{j i}$ is also obtained from these rows, thus $A$, and the product matrix ($p_{i j}$) is symmetric. Similarly, the product $p_{i j} = p_{j i}$ is a symmetric matrix.

A quick proof of the symmetry of $A^{T} A$ results from the fact that it is its own transpose:
 * $$\left(\mathbf{A} \mathbf{A}^\operatorname{T}\right)^\operatorname{T} = \left(\mathbf{A}^\operatorname{T}\right)^\operatorname{T} \mathbf{A}^\operatorname{T}= \mathbf{A} \mathbf{A}^\operatorname{T} .$$

Implementation of matrix transposition on computers
On a computer, one can often avoid explicitly transposing a matrix in memory by simply accessing the same data in a different order. For example, software libraries for linear algebra, such as BLAS, typically provide options to specify that certain matrices are to be interpreted in transposed order to avoid the necessity of data movement.

However, there remain a number of circumstances in which it is necessary or desirable to physically reorder a matrix in memory to its transposed ordering. For example, with a matrix stored in row-major order, the rows of the matrix are contiguous in memory and the columns are discontiguous. If repeated operations need to be performed on the columns, for example in a fast Fourier transform algorithm, transposing the matrix in memory (to make the columns contiguous) may improve performance by increasing memory locality.

Ideally, one might hope to transpose a matrix with minimal additional storage. This leads to the problem of transposing an n × m matrix in-place, with O(1) additional storage or at most storage much less than mn. For n ≠ m, this involves a complicated permutation of the data elements that is non-trivial to implement in-place. Therefore, efficient in-place matrix transposition has been the subject of numerous research publications in computer science, starting in the late 1950s, and several algorithms have been developed.

Transposes of linear maps and bilinear forms
As the main use of matrices is to represent linear maps between finite-dimensional vector spaces, the transpose is an operation on matrices that may be seen as the representation of some operation on linear maps.

This leads to a much more general definition of the transpose that works on every linear map, even when linear maps cannot be represented by matrices (such as in the case of infinite dimensional vector spaces). In the finite dimensional case, the matrix representing the transpose of a linear map is the transpose of the matrix representing the linear map, independently of the basis choice.

Transpose of a linear map
Let $A A^{T}$ denote the algebraic dual space of an $R$-module $X$. Let $X$ and $Y$ be $R$-modules. If $X^{#}$ is a linear map, then its algebraic adjoint or dual, is the map $u : X → Y$ defined by $u^{#} : Y^{#} → X^{#}$. The resulting functional $f f ∘ u$ is called the pullback of $f$ by $u$. The following relation characterizes the algebraic adjoint of $u$
 * $u^{#}(f)$ for all $⟨u^{#}(f), x⟩ = ⟨f, u(x)⟩$ and $f ∈ Y^{#}$

where $x ∈ X$ is the natural pairing (i.e. defined by $⟨•, •⟩$). This definition also applies unchanged to left modules and to vector spaces.

The definition of the transpose may be seen to be independent of any bilinear form on the modules, unlike the adjoint (below).

The continuous dual space of a topological vector space (TVS) $X$ is denoted by $⟨h, z⟩ := h(z)$. If $X$ and $Y$ are TVSs then a linear map $X'$ is weakly continuous if and only if $u : X → Y$, in which case we let $u^{#}(Y) ⊆ X$ denote the restriction of $^{t}u : Y → X$ to $u^{#}$. The map $Y'$ is called the transpose of $u$.

If the matrix $^{t}u$ describes a linear map with respect to bases of $V$ and $W$, then the matrix $A$ describes the transpose of that linear map with respect to the dual bases.

Transpose of a bilinear form
Every linear map to the dual space $A^{T}$ defines a bilinear form $u : X → X^{#}$, with the relation $B : X × X → F$. By defining the transpose of this bilinear form as the bilinear form $^{t}B$ defined by the transpose $B(x, y) = u(x)(y)$ i.e. $^{t}u : X^{##} → X^{#}$, we find that $^{t}B(y, x) = ^{t}u(Ψ(y))(x)$. Here, $Ψ$ is the natural homomorphism $B(x, y) = ^{t}B(y, x)$ into the double dual.

Adjoint
If the vector spaces $X$ and $Y$ have respectively nondegenerate bilinear forms $X → X^{##}$ and $B_{X}$, a concept known as the adjoint, which is closely related to the transpose, may be defined:

If $B_{Y}$ is a linear map between vector spaces $X$ and $Y$, we define $g$ as the adjoint of $u$ if $u : X → Y$ satisfies
 * $$B_X\big(x, g(y)\big) = B_Y\big(u(x), y\big)$$ for all $g : Y → X$ and $x ∈ X$.

These bilinear forms define an isomorphism between $X$ and $y ∈ Y$, and between $Y$ and $X^{#}$, resulting in an isomorphism between the transpose and adjoint of $u$. The matrix of the adjoint of a map is the transposed matrix only if the bases are orthonormal with respect to their bilinear forms. In this context, many authors however, use the term transpose to refer to the adjoint as defined here.

The adjoint allows us to consider whether $Y^{#}$ is equal to $g : Y → X$. In particular, this allows the orthogonal group over a vector space $X$ with a quadratic form to be defined without reference to matrices (nor the components thereof) as the set of all linear maps $u^{ −1} : Y → X$ for which the adjoint equals the inverse.

Over a complex vector space, one often works with sesquilinear forms (conjugate-linear in one argument) instead of bilinear forms. The Hermitian adjoint of a map between such spaces is defined similarly, and the matrix of the Hermitian adjoint is given by the conjugate transpose matrix if the bases are orthonormal.

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: Transpose


text:
Tottenham Court Road station

Tottenham Court Road is an interchange station in the West End of London for London Underground and Elizabeth line services.

The London Underground station is served by the Central and Northern lines. On the Central line it is between Oxford Circus and Holborn stations, and on the Charing Cross branch of the Northern line it is between Goodge Street and Leicester Square stations. The Elizabeth line station is between Bond Street and Farringdon stations.

The station is located at St Giles Circus, the junction of Tottenham Court Road, Oxford Street, New Oxford Street and Charing Cross Road and is in Travelcard Zone 1, with a second entrance at Dean Street.

Central London Railway
The station opened as part of the Central London Railway (CLR) on 30 July 1900. From that date until 24 September 1933, the next station eastbound on the Central line was the now-defunct ; the next stop in that direction is now. The platforms are under Oxford Street west of St Giles' Circus and were originally connected to the ticket hall via lifts at the east end of the platforms. The original station building was on the south side of Oxford Street and was designed in common with other CLR stations by Harry Bell Measures. The building and its neighbours were demolished in 2009.

Charing Cross, Euston & Hampstead Railway
The Charing Cross, Euston & Hampstead Railway (CCE&HR, now part of the Northern line) arrived here on 22 June 1907 but used the name Oxford Street until an interchange (linking the eastbound Central line with the southbound Northern line via the ends of the platform) was opened on 3 September 1908 from when the present name was used for both lines. The next station north on the Northern line was originally called Tottenham Court Road, but was renamed to at this time.

The original ticket office was directly beneath St Giles circus and was accessed from stairs on three street corners around the Circus. Its original lift shafts and emergency stairs are still extant. A set of emergency stairs can be used as access down to the ends of the Northern line platform. The lift shafts are used for offices and station facilities.

Early improvements
Like a number of other central area stations, Tottenham Court Road underwent improvements during the 1920s to replace the original sets of lifts with escalators. Works commenced in 1923; a new subsurface ticket hall, under St Giles Circus, was constructed and the escalators came into service on 28 September 1926 (upper set) and 1 February 1926 (lower set). A shaft for three escalators was driven from the ticket hall under the junction down to the east end of the Central line platforms ending at an intermediate circulation space. A further pair of escalators descend from this level to the north end of the Northern line platforms. The lifts were removed and the redundant shafts were used as ventilation ducts. In 1938 a chiller plant began operating at the station. This was decommissioned in 1949.

Passenger congestion entering and leaving the Northern line platforms was partially eased by the addition of a short single escalator at the centre of the platform leading up to a passageway linking to the intermediate circulation area. However, this was in itself a cause of congestion, as traffic trying to leave the station from the Northern line found itself in the path of traffic entering and travelling to the Central line.

In the early 1980s, the entire station was redecorated, losing the distinctive Leslie Green-designed platform tiling pattern of the Yerkes tube lines (which included the CCE&HR), and the plain white platform tiles of the CLR. It was replaced by distinctive mosaics by Eduardo Paolozzi, located on platforms, passages and escalator entrances.

Initial plans for station expansion
The station had four entrances to the sub-surface ticket hall from the north-east, south-west and north-west corners of the junction and from a subway beneath the Centre Point building which starts on Andrew Borde Street. The entrances were frequently congested leading to occasions during peak periods of the day when they were briefly closed to prevent overcrowding in the station.

In the aftermath of the King's Cross fire in 1987, London Underground was recommended to investigate "passenger flow and congestion in stations and take remedial action". A Parliamentary bill was tabled in 1991 to permit London Underground to improve and expand the frequently congested station, however this was not proceeded with. In 2000, London Underground consulted on a station upgrade including a new larger ticket hall, new escalators and step free access, which would have taken 4 years to construct.

Expansion as part of Crossrail

The station was eventually reconstructed and upgraded in the mid 2010s as part of the Crossrail project to construct the Elizabeth line, with the £500million station upgrade taking eight years. To enable the station expansion work to occur, both the Astoria theatres and the original Central line entrance were demolished. During construction, the Central and Northern lines were alternately closed for several months to allow for upgrade works to take place.

Upon completion in 2017, the project delivered:

 * A new ticket hall six times larger than previous, located below St Giles Circus and the forecourt of Centre Point
 * New public plaza outside Centre Point, with station entrances designed by Hawkins\Brown
 * New dedicated set of escalators to access the Northern line
 * New and expanded passageways underground
 * Escalators down to the eastern end of the future Elizabeth line station.
 * Step-free access throughout the station
 * Restoration of existing artwork by Eduardo Paolozzi, and a new artwork in the ticket hall by Daniel Buren

On Dean Street, a dedicated western entrance and ticket hall was built to access the new Elizabeth line platforms. These platforms stretch for 230 m between the two ticket halls, underneath Soho Square. The completed western entrance and Crossrail platforms were handed over to TfL in early 2021. Crossrail links Tottenham Court Road to Canary Wharf, Abbey Wood, Stratford, and Shenfield in the east with Paddington, Heathrow and Reading in the west. The central section of the Elizabeth line opened on 24 May 2022 between Paddington and Abbey Wood. Direct service to Reading, Heathrow, Stratford and Shenfield commenced on 6 November 2022.

As part of a plan to raise £500million from development above new Crossrail stations, a residential development of 92 homes as well as retail units will be built above the western ticket hall by developer Galliard Homes and a new West End theatre as well as retail and office space will be built above the eastern ticket hall by developer Derwent London. The new theatre will be the first West End theatre to open in over 50 years.

Artworks
In the mid 1980s, Eduardo Paolozzi was commissioned to create an artwork for the station. The design includes panels of tessellated and hand-cut smalti mural mosaic, and is a distinct and noticeable feature of the station. The frenetic design was intended to reflect the station's position adjacent to Tottenham Court Road's large concentration of hi-fi and electronics shops. During the expansion of the station for Crossrail, sections of the mosaic were restored, moved or replaced while other section were destroyed, some sections of which have been removed to be conserved at the University of Edinburgh.

As part of the expansion of the Eastern ticket hall, Art on the Underground commissioned an artwork by Daniel Buren, a French conceptual artist. This work, Diamonds and Circles', works 'in situ, was Buren's first permanent public commission in the UK. It comprises colourful diamond and circle shapes, which contrast with Buren's trademark stripes in black and white, fixed to internal glass walls throughout the ticket hall. The artwork was completed in 2017.

As part of the Crossrail project, two artworks were commissioned by Turner Prize–winning artists, one for each ticket hall. At the eastern ticket hall, Richard Wright created a mural of geometric patterns in gold leaf on the concrete ceiling above the Crossrail escalators. At the western ticket hall, Douglas Gordon installed a video artwork above the escalators, involving Gordon's giant blinking eye with names of Soho establishments that no longer exist reflected in it.

Services
Services at Tottenham Court Road are operated by the Elizabeth line, and London Underground's Central and Northern lines.

The typical off-peak service in trains per hour (tph) is:

The station also served by a night service on Friday and Saturday nights as part of the Night Tube. The station is served by Central line trains every 10 minutes in each direction and Northern line trains every 7-8 minutes in each direction.

Crossrail 2
The Crossrail 2 project proposed a station at Tottenham Court Road, the only planned interchange between the Elizabeth line and Crossrail 2. The expanded station built as part of the Crossrail project took the future demands of Crossrail 2 into account, which will allow for less construction disruption if the line is built. The proposals involve a new Crossrail 2 ticket hall on the site of Curzon Soho on Shaftesbury Avenue. This has been criticised by campaigners. The station and ticket hall site were first safeguarded as part of the route during the development of the Chelsea-Hackney line in 1991. In November 2020, plans for Crossrail 2 were shelved.

In popular culture

 * The station was used for a sequence in the 1981 film An American Werewolf in London.
 * A scene in the 2008 film The Bank Job is set in the station, though it was shot at Aldwych tube station.
 * A scene in the musical We Will Rock You is set in the station; the musical played across the street at the Dominion Theatre from 2002 to 2014.

Connections
London Buses day and night routes serve the station.

title: Tottenham Court Road station


text:
Bluebell Railway

The Bluebell Railway is an 11 mi heritage line in West Sussex in England. It is managed by the Bluebell Railway Preservation Society. It uses steam trains which operate between Sheffield Park and East Grinstead, with intermediate stations at Horsted Keynes and Kingscote.

It is the first preserved standard gauge steam-operated passenger railway in the world to operate a public service. The society ran its first train on 7 August 1960, less than three years after the line from East Grinstead to Lewes had been closed by British Railways.

On 23 March 2013, the Bluebell Railway started to run through to its new East Grinstead terminus station. At East Grinstead there is a connection to the national rail network, the first connection of the Bluebell Railway to the national network in 50 years, since the Horsted Keynes – Haywards Heath line closed in 1963.

Today the railway is managed and run largely by volunteers. Having preserved a number of steam locomotives even before steam stopped running on British mainline railways in 1968, today it has over 30 steam locomotives, the 2nd largest collection in the UK after the National Railway Museum. The Bluebell also has almost 150 carriages and wagons, most of them pre-1939.

History
In 1877 an act of Parliament authorised construction of the Lewes and East Grinstead Railway (L&EGR). The line was sponsored by local landowners, including the Earl of Sheffield. A year later another act enabled the London, Brighton and South Coast Railway Company (LB&SCR), chaired by Samuel Laing, to acquire and operate the line.

The line had six stations, but only Barcombe was within walking distance of a village. Chailey parish had two stations, one at Sheffield Park and the other at Newick and Chailey. It was customary for a rural line supported by a company or individuals to have stations close to the residences of its sponsors. Thus Sheffield Park station was built for the Earl of Sheffield, and Newick and Chailey for Newick Park and Reedens, the homes of two other sponsors. The other stations were at Kingscote, West Hoathly and Horsted Keynes. A branch ran from a junction at Horsted Keynes to Ardingly and Haywards Heath on the LB&SCR main line.

The 1877 and 1878 acts included a clause that:

This imposed a legal requirement to provide a service, and the only way to remove this obligation was to pass another act.

Designed under instructions from LB&SCR Chief Engineer Frederick Banister, the line was constructed to take double track. However, only the section between East Grinstead and Horsted Keynes (and thence to Haywards Heath via Ardingly) was laid as such; south of the junction at Horsted Keynes the line was single track with passing loops at stations. The line was opened in 1882.

Goods traffic on the line consisted of local produce; milk: farm products and coal, and timber to and from Albert Turner & Son, a sawmill. The only time Sheffield Park received a substantial number of passengers was when Lord Sheffield entertained the Australian cricket team, with a match between them and Lord Sheffield's own team.

Accident
On 31 July 1943, newlyweds Ronald Knapp and Winifred Standing were killed when they were pulled under a train from Lewes to East Grinstead. The couple walked along the railway on a dark rainy night. When the train got to Horsted Keynes, the guard found a raincoat covered with blood on the engine. Another coat was found near two bodies in the middle of the tracks. The ganger who found them told the inquest the couple must have been walking with their backs to the train.

"There was a very heavy squall at the time and the couple would probably have not heard a thing," he said. The coroner said Ronald and Winifred were trespassing and no blame could be attached to any railway worker. Little more than a week after they were married, the couple's funeral was at St Giles' Church, Horsted Keynes, where they are buried together in a grave marked by a War Graves Commission headstone.

Closure
In 1954, long before the Beeching Axe, the branch line committee of British Railways proposed closing the line from East Grinstead to Culver Junction near Lewes. This was challenged by local residents, but closure was agreed in February 1955 for 15 June 1955, although the line closed on 29 May due to a rail strike. An acrimonious battle between British Railways and the users of the Bluebell Line then ensued, and lasted three years.

Shortly after closure, Margery Bessemer of Chailey discovered in the 1877 and 1878 acts the clause relating to the "Statutory Line", and demanded British Railways reinstate services. On 7 August 1956 British Railways reopened the line, with trains stopping at stations mentioned in the acts. British Railways took the case to the House of Commons in 1957, resulting in a public inquiry. British Railways were censured, but later the Transport Commission persuaded Parliament to repeal the special section of the act. By this means the line was finally closed on 17 March 1958.

Preservation
On 15 March 1959 a group that included the future president of the society, Bernard Holden, met in Ardingly and formed the Lewes and East Grinstead Railway Preservation Society. The society elected John Leroy as the first chairman, and £940 was raised in donations to start the society. On a vote at the meeting, the society changed its name to the Bluebell Railway Preservation Society.

The society's initial aim was to reopen the whole line from East Grinstead to Culver Junction as a commercial service, using a two-car DMU. The plans came to nothing: the society failed to buy the whole line, and most local residents were not interested. The committee then recommended that the stretch of track between Sheffield Park and Horsted Keynes could be run as a tourist attraction, with vintage locomotives and stock operated by unpaid volunteer staff.

Sheffield Park to Horsted Keynes
As BR still ran an electrified line from Horsted Keynes to Ardingly, the society leased a stretch of track from BR just south of this. In 1960, the interim line was opened, running from Sheffield Park to Bluebell Halt, 100 yard south of Horsted Keynes. In 1962, the society extended services to Horsted Keynes. Also in 1962, a halt was opened at Holywell (Waterworks). However, this was closed the following year. BR withdrew passenger services from Horsted Keynes to Haywards Heath in 1963; and with complete closure of the line north of Horsted Keynes, the Bluebell Line was severed from the BR system.

Horsted Keynes to Kingscote
In 1974 the society purchased the freehold of the demolished West Hoathly station, allowing the first steps to be taken towards an extension northwards towards East Grinstead station. It then purchased the freehold of the site of Kingscote station in January 1985. These efforts culminated in a public inquiry, with the Secretaries of State for the Environment and Transport giving planning permission and a Light Railway Order for an extension to East Grinstead in 1985.

The Bluebell Railway Preservation Society completed the extension from Horsted Keynes to Kingscote in April 1994, re-laying track through Sharpthorne Tunnel, which at 731 yd is the longest on a UK heritage railway. At the north end of Sharpthorne Tunnel, the line passes through the site of the former West Hoathly railway station. It was demolished in 1967, but remains of the platforms and goods dock are still visible.

2010 marked the Bluebell's 50th anniversary of running trains. To mark the event, the railway held a gala over 6–8 August 2010 with all available home engines and two visitor engines. Some of the society's founder members gathered at Horsted Keynes to mark the arrival of a commemorative LB&SCR A1X class No.55 Stepney-hauled steam train. The entourage then travelled towards Sheffield Park.

Kingscote to East Grinstead via Imberhorne
From its inception, the society had always planned to work northwards towards East Grinstead, where the line would connect with the national network. BR donated Imberhorne Viaduct to the railway in 1992, but the purchase of the final pieces of the by then privately owned track bed north to East Grinstead was only completed in 2003, allowing physical civil engineering activity to be undertaken from that year.

A major problem was the former landfill site in the 30 ft cutting just south of Imberhorne Viaduct. It had been filled with domestic waste by East Grinstead Town Council in the 1960s and 1970s, but tests undertaken by contractors working for both the society and the borough council found the 96000 m3 of waste within the 500 m cutting were not toxic.

The excavated clay-cap covering the landfill site was taken south by rail, to fill the site of a removed viaduct and embankment on the old Ardingly spur. In January 2008 agreement was given to start clearing foliage on the section of the tip between Imberhorne Lane and Hill Place bridges. In a public launch event, BBC news reader Nicholas Owen—a local resident and society volunteer—started removal of the actual waste on 25 November 2008.

Initially rubbish was removed from the site by lorry, but, due to the substantial volume and cost of about £45/tonne, in 2009 a trial removal of spoil by rail was carried out by DB Schenker Rail (UK). At £25,000 per train and now undertaken by GB Railfreight, this practice continued periodically as funds became available. However, an increase in the landfill tax was announced in 2008, and this was due to take effect from April 2012. It would increase the cost of removal from £25/tonne to £90/tonne. So the society formed an appeal to complete the removal of the landfill waste by the end of March 2012. With the receiving site changed to Appleford, Oxfordshire and thanks to the "tenner for the tip" appeal, the cash target was met and the rubbish was removed by rail in time.

In autumn 2008 work started on site clearance at East Grinstead for construction of the new station about 100 yd south of the national rail station. At the railway's 50th anniversary celebration weekend in 2010, East Sussex resident Dame Vera Lynn launched a £3.8 million appeal; the greater part of this amount would be put towards reconnecting the line to East Grinstead. Mid Sussex District Council responded with a one-off donation of £50,000 towards the reconnection.

On 7 March 2013, the last section of track was formally joined using a white fishplate, with the honour of tightening the four bolts being given to Barbara Watkins, a long-standing Bluebell Railway volunteer. The extension to East Grinstead was officially opened on Saturday 23 March, with a two-week opening festival starting that day.

West: Horsted Keynes to Haywards Heath via Ardingly
Originally built as a double-track line, it was electrified in the 1930s, with 2-NOL units used for the Seaford-Horsted Keynes service. The line between Horsted Keynes and Ardingly was operated as single-track in its final years, with 2-BIL/Class 401 and 2-HAL/Class 402 units. The second track was left in place and used for carriage storage, most notably the new Kent Coast electric stock prior to its introduction and later the steam-hauled stock that it replaced.

After the line's closure in 1963, the trackbed was purchased in its entirety by a member of the local gentry. In the 1990s the society bought the abandoned trackbed west between Horsted Keynes and Ardingly from his estate. This included up to the Hanson Aggregates depot built on the former Ardingly railway station site.

The society plans to reconnect the line with Network Rail at Copyhold Junction, to allow access to the London to Brighton Main Line. Stations could either be located at Copyhold or Haywards Heath. There is a proposal that the line could be restored as third rail electrified, allowing operation of the society's electric stock.

While the 218 yard Lywood Tunnel remains in good condition, there are two major areas of work that would be required to re-open the line, these being the replacement of a short girder-bridge span bridge and the 117 yard Sheriff Mill Viaduct, which was demolished in 1969. The removed clay-cap from Imberhorne cutting has been deposited on the banks of the former Sherriff Mill viaduct to allow later bridging of the gap. Also in 2013, the former Tewkesbury and Malvern Railway bridge that crossed over the M50 motorway were donated to the railway for eventual installation in the replacement bridge.

South: Sheffield Park to Lewes
By the late Victorian era, Lewes station was the convergence point of three lines from the East Sussex coast and three lines to the north all of which reached London via Croydon. Today, Lewes has a line to the north which joins the Brighton main Line at Burgess Hill and from there on to Gatwick Airport, East Croydon and London, a line west towards Brighton, a line south to Newhaven and Seaford, and a line east to Eastbourne, Hastings and Ashford.

Originally the Bluebell Line was the straightest and quickest route from Lewes to London. The Bluebell Railway ran directly south from Sheffield Park to Culver Junction (at Culver Farm just south of Barcombe Mills), with intermediate stations at Newick and Chailey and Barcombe. At Culver Junction it joined the 1858 Wealden Line (part of which is now restored as the nearby Heritage Lavender Line), thereby gaining access to Lewes. The section from East Grinstead to Culver Junction was closed in 1958, and the Lewes to Uckfield line in 1969 by British Rail.

Bluebell supporters and committee members have expressed interest in re-building the line south by three more stations to Lewes. However, a substantial number of large civil engineering obstacles and intrusions onto the former trackbed make this a difficult project to envisage the completion of. For execution, the project would require: The remaining undeveloped line from Lewes to Sheffield Park has been safeguarded as a bridleway and footpath.
 * The bridging of the raised, widened and re-aligned A275 road immediately south of Sheffield Park
 * The re-excavation of waste-infill under the former road bridges just south of Sheffield Park and Barcombe stations
 * The in-filling since of the cutting and former route under the A272 road
 * The re-excavation of waste-infill at the former Newick and Chailey, which includes industrial waste producing large amounts of methane gas discharges
 * The fact that a large private housing estate has been built on and surrounding the former Newick and Chailey site

Stations
The various stations have been restored to show different periods of the railway's life:
 * Sheffield Park has been restored to a Victorian ambience, as it would have appeared during the time of the London, Brighton and South Coast Railway (up to 1922)
 * Horsted Keynes emulates the Southern Railway from 1923 to 1947
 * West Hoathly (if built) will emulate the British Railways of the late 1940s
 * Kingscote echoes the British Railways of the 1950s
 * East Grinstead is an amalgam of British Railways of the 1950s and 1960s

Heritage railway

 * East Grinstead to Sheffield Park
 * East Grinstead
 * Kingscote
 * West Hoathly (closed)
 * Horsted Keynes
 * Bluebell Halt (closed)
 * Holywell (Waterworks) (closed)
 * Freshfield Halt (closed)
 * Ketches Halt (closed)
 * Sheffield Park
 * Horsted Keynes to Ardingly (proposed)
 * Horsted Keynes
 * Ardingly (proposed)

Original stations

 * Lewes to East Grinstead (Low Level)
 * East Grinstead
 * Kingscote
 * West Hoathly
 * Horsted Keynes
 * Sheffield Park
 * Newick and Chailey
 * Barcombe
 * Lewes

Rolling stock
The Bluebell Railway preserved a number of steam locomotives before the cessation of steam service on British mainline railways in 1968. Today it has the largest collection - over 30 - of steam locomotives in the UK after the National Railway Museum (NRM). The society also has a collection of almost 150 carriages and wagons, most of them pre-war. A project is under way to recreate a long-lost type of locomotive (LB&SCR H2 class Atlantic) from a few surviving parts.

In April 2008, the Heritage Lottery Fund provided a £2.8M grant towards new buildings next to Sheffield Park, to provide weatherproof shelter for up to 17 carriages. The funds were also used to: create a museum and interpretation area; create new facilities for locomotive crews; create a rainwater catchment system from the roof of the carriage building, which is then processed and used to fill the steam engines' boilers; restore the railway's historic platform buildings.

Twinning
The Bluebell Railway is twinned with the Museumstoomtram Hoorn – Medemblik, which links Hoorn and Medemblik, North Holland, the Netherlands.

title: Bluebell Railway