Talk:Matrix (mathematics)/GA1

GA Review

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I will be reviewing this article. This will be my first review so bear with me Jakob. (TimothyRias (talk) 14:56, 21 April 2009 (UTC))

Preliminary thoughts: Looks like Jakob has produced another fine article. I will give a detailed review tomorrow. (TimothyRias (talk) 15:16, 21 April 2009 (UTC))

TR GA review

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My overall impression is that the article is very close to GA, except for some minor details mentioned below.

1. Is it reasonably well written?

   A. Prose quality:

   The prose of the article is generally OK. My main concern is that the article features some very short and oneline paragraphs. These can probably be fixed by better integrating them in the surrounding text.

   I'm also concerned about the amount of unexplained jargon in the history section. I have a background in mathematics, and even for me this section was sort of hard to read. I know it is somewhat inevitable, but it might help if the significance of the mentioned notions and theorems was somewhat elaborated on.

   The most pressing issues have been dealt with. The whole article can use some polishing before FA, but is certainly good enough for GA.(TimothyRias (talk) 07:13, 27 April 2009 (UTC))

   B. MoS compliance:

   The article has some MoS issues. The main one being formula interpunction. Formulas always need correct interpunction. I have corrected some cases, but the whole article needs another thorough check. Note that per WP:MOSMATH the interpunction needs to be inside math tags when used.

   A more specific concern is the layout in the definition section. It might be better to have the text and the matrix examples on different lines.

2. Is it factually accurate and verifiable?

   A. References to sources:

   Most statements that need referencing have been referenced. (I have added a couple of citation needed templates to statements that in my opinion need a reference.)

   B. Citation of reliable sources where necessary:

   references are mostly well established textbooks, so no problems here.

   C. No original research:

3. Is it broad in its coverage?

   A. Major aspects:

   The text covers all the major aspects of matrices.

   B. Focused:

   without going to much in detail, applying summary style where appropriate.

4. Is it neutral?

   Fair representation without bias:

5. Is it stable?

   No edit wars, etc:

   The article has been on my watchlist for sometime, with no major disruptive edits.

6. Does it contain images to illustrate the topic?

   A. Images are copyright tagged, and non-free images have fair use rationales:

   checked.

   B. Images are provided where possible and appropriate, with suitable captions:

   OK

7. Overall:

   Pass or Fail:

Some more comments

Some specific comments/questions about the contents

• Are tensors really a generalization of matrices? A normally think of them as the generalization of linear maps.

• Well I think it's kind of both. However, in trying to keep things as elementary as possible, I would prefer emphasizing the relation to matrices in this article. "tensors [...] can be seen as higher-dimensional arrays of numbers" should be OK, right? Jakob.scholbach (talk) 19:08, 22 April 2009 (UTC)

• Sure that will do.(TimothyRias (talk) 19:56, 22 April 2009 (UTC))

• The section about linear transformations mentions nullity without ever explaining what this is.

• It says "The nullity [...] of a matrix A are the dimension of the kernel [...] of the linear map represented by A, respectively." Jakob.scholbach (talk) 19:08, 22 April 2009 (UTC)

• I read that sentence as X and Y in the case of matrices correspond to A and B in case of linear maps, although I guess it can also function as a definition of X and Y. May be there is a way to make this more explicit? (TimothyRias (talk) 19:56, 22 April 2009 (UTC))

• I get it. Will fix. Jakob.scholbach (talk) 13:40, 25 April 2009 (UTC)

I have reconsulted the references. Except for the Brown reference which defines the nullity as the dimension of the kernel, none of Bretscher, Greub, Horn&Johnson, Golub&Van Loan, Lang (LA) even mention this notion. Somehow, the nullity seems to be much less of a separate notion than the rank. Perhaps this is because the column rank = row rank? I have tried to reflect this state of affairs by toning the relevance of nullity a bit down. Do you think this is OK? Jakob.scholbach (talk) 18:55, 26 April 2009 (UTC)

OK. (TimothyRias (talk) 07:09, 27 April 2009 (UTC))

• The trace of a matrix is now only mentioned in the section on eigenvalues. It might be useful to mention this on a separate occasion and elaborate a little on the significance. (Also note that the trace is only equal to the sum of the eigenvalues if the multiplicity of the eigenvalues is taken into account, this not clear from the text.)

• Right. Will fix. Jakob.scholbach (talk) 19:08, 22 April 2009 (UTC)

I have moved the mention of the trace up to the beginning of the section. (For now, I removed the relation to sums of eigenvalues, since we would have to talk about algebraic and geometric multiplicities, too.) Jakob.scholbach (talk) 13:40, 25 April 2009 (UTC)

This is OK for GA. It would probably be good to try to improve the treatment of trace before taking this to FA. (TimothyRias (talk) 07:09, 27 April 2009 (UTC))

• In the section on eigenvalues it is never made explicit that n is the dimension of the matrix.

• Fixed. Jakob.scholbach (talk) 19:08, 22 April 2009 (UTC)

• In the same section, it might also not be clear to all readers what is meant by p(A).

• OK. I've put a brief explanation. The reader will find a longer one in the subarticle. Jakob.scholbach (talk) 19:08, 22 April 2009 (UTC)

OK.(TimothyRias (talk) 07:09, 27 April 2009 (UTC))

• It might be worthwhile to mention singular value decomposition in the section in the section on decomposition, since it is referred to latter in the examples.

• Done (briefly.) Jakob.scholbach (talk) 13:40, 25 April 2009 (UTC)

Briefly is fine. (TimothyRias (talk) 07:09, 27 April 2009 (UTC))

• Should the application of matrices in the matrix models of in string theory be mentioned in the applications section?

• Do you think it's off-topic? Credits for the physics stuff go to Markus Poessel who wrote that, but I personally think it fits nicely. Unless we have space problems (which we don't have yet), I would leave it.

• The article doesn't mention matrix string theory, does it? My suggestion is that maybe it should. But, I guess that the article has to be a little selective with the examples it uses. (TimothyRias (talk) 20:08, 22 April 2009 (UTC))

Anyway, this more of a suggestion for FA than the current GA review. (TimothyRias ([[User

talk:TimothyRias|talk]]) 14:43, 23 April 2009 (UTC))

Sorry, I was blind. I thought you were talking about removing some stuff. So, in principle I'm open to all sorts of additions. (You will also have remarked Proteins' suggestions for further material.) I would suggest we sit down at some point and figure out what and how to make a comprehensive applications section. I foresay that we might want to highlight certain features, in order to avoid a long and arid "disambiguation list", but we can see that later. Jakob.scholbach (talk) 13:40, 25 April 2009 (UTC)

This definitely needs some atention for FA, but is OK for now. (TimothyRias (talk) 07:09, 27 April 2009 (UTC))

• 1A: I found one short paragraph and eliminated that one. There are many short "paragraphs" but this is due to mathematical formulae interspersing. I agree it looks a bit ragged here and there, but I don't know what to do about it. What do you think?

I have tried to make the history section a bit more welcoming. I think we should not afford to explain here the terms that are explained later, so, for example, determinants are not explained. Are there any particular points left that you think need more care? Jakob.scholbach (talk) 19:37, 22 April 2009 (UTC)

The history section has been moved down. While I slightly disliked the move initially, it does have the advantage that most terms showing up down there have been explained in the foregoing text. I have tried to make it more accomodating. OK now? Jakob.scholbach (talk) 13:40, 25 April 2009 (UTC)

• 1B: Fixed.
• 2A: Referenced the etymology claim.

Thank you much, Timothy, for your review. Jakob.scholbach (talk) 19:08, 22 April 2009 (UTC)