Wikipedia:Peer review/Matrix (mathematics)/archive1

Matrix (mathematics)

• A script has been used to generate a semi-automated review of the article for issues relating to grammar and house style; it can be found on the automated peer review page for May 2009.

This peer review discussion has been closed.
I've listed this article for peer review because I want to improve it to meet FA criteria. I want to post it to FAC, but not now. I want some comments on how to improve it to meet FA criteria. Also, I am gathering Wikipedians to improve it. Leave a message on my talk page if you are interested.

Thanks, Visit me at Ftbhrygvn (Talk|Contribs|Log|Userboxes) 15:39, 30 May 2009 (UTC)

In the lead I would quible about

Matrices consisting of only one column or row are called vectors

vectors are really one-dimensional arrays rather than degenerate two dimensional arrays. I also thing mention vectors and tensors is too high in lead as the article starts by saying what matricies are not.--Salix (talk): 06:27, 3 June 2009 (UTC)

The box on positive and negative quadratic forms takes quite a few logical jumps. From matrix to quadratic eqn to ellipse/hyperbola. I think a bit more explination could be useful here.--Salix (talk): 06:33, 3 June 2009 (UTC)

• Hmmm... I tend to mistrust "are really" in an encyclopedic context. Row vectors and column vectors are degenerate two dimensional arrays, their two-dimensionality being heavily influenced by the two-dimensional paper we write on (historically) and (more recently) the two-dimensional computer screens we read. As for "vectors", well, these "are really" directed magnitudes, elements of a vector space, or disease transmittors. :-) Geometry guy 21:40, 12 June 2009 (UTC)

Comments from Geometry guy

(All editors are welcome to contribute to this section)

• Initial comments. This is a challenging article to bring to FA. It has had many beneficial contributions from editors like Jakob Scholbach, who is an expert on bringing mathematics articles to FA. However, the current article is a mess: in the words of a country yokel being asked for directions, "if I were wanting to bring this article to FA, I wouldn't start from here". But start from here we must. Geometry guy 21:57, 12 June 2009 (UTC)
• The challenge. The challenge for this article is that the notion of a matrix is utterly elementary. An intelligent 12 year old should be able to grasp it, and we hope that most 18 year olds can. Some parts of this article may only be accessible to mathematics graduates, but most of it has a broad audience. Geometry guy 22:13, 12 June 2009 (UTC)
• The lead. Issues concerning the lead should be fixed last, but I'm bringing them up now, because similar problems occur throughout the article. First sentence "is a rectangular array of numbers, as shown at the right." Actually on the right I see a rectangular array of letters decorated by subscripts; I must be too stupid to understand this article. Second sentence (see above): matrices and one dimensional arrays represent geometrical notions such as vectors, linear transformations, bilinear forms and tensors; they are not equivalent to such concepts. Third sentence: the relation between linear transformations and matrices has not yet been explained or even defined. Fourth sentence: "usual identities" not explained; the identity "AB=BA" need not even make sense. Geometry guy 22:13, 12 June 2009 (UTC)
• Further comments. In the absence of any substantial response, I will just add briefly some other things I noticed on my read through.
  • Most of this article focuses on real and complex matrices,... seems to be an unhelpful and inaccurate selfref: most of the matrices in the article have integer entries.
  • There are WP:ACCESS issues with the examples of linear transformations: in particular, the black dot (origin) is hard to see.
  • The fact that a right inverse is an inverse for square matrices is a triumph of linear algebra, and should not be made into a definition or noted without comment.
  • The fact that tr(AB)=tr(BA) does not need a specific citation: it needs a formula which shows they are manifestly the same.
  • The first paragraph on the determinant is opaque unless the reader already knows what it means.
  • The last paragraph on the determinant should probably mention that Gaussian elimination is generally more efficient than Cramer's rule.
  • There is very little on row/column operations and Gaussian elimination: these are an essential part of what matrices are for.
  • It may be worth discussing eigenspaces and the primary decomposition theorem.
  • The Computational aspects section has too much digressive material on computing and numerical analysis: BASIC ROMS of the 1970s are decidedly off-topic.
  • The first paragraph of Abstract algebraic aspects and generalizations is a mini-lead and is mostly unhelpful e.g., "Matrices, subject to certain requirements tend to form groups known as matrix groups." conveys almost no information and personifies the topic.

Good luck improving the article. Geometry guy 17:44, 21 June 2009 (UTC)