Wikipedia:WikiProject Mathematics/A-class rating/Singular value decomposition

Singular value decomposition
review Nominated by: Paolo.dL (talk) 14:59, 14 February 2011 (UTC)


 * I recently did a few adjustments to this article. Mainly, I edited the "Intuitive interpretations" section. However, my contribution was only a fraction of the work needed to make the article so complete and well written. The figure in the introduction, for instance, is an outstanding example of intuitively appealing geometrical interpretation, understandable by non-mathematicians. The introduction is simple, short, and effective. In my opinion, Eigenvalues and eigenvectors was worst than this article when it gained featured article status. Paolo.dL (talk) 15:12, 14 February 2011 (UTC)


 * Comment. The article currently lacks a developed lead (see WP:LEAD).  This is an obvious no-go.  There are entire sections lacking inline references as well.  Sławomir Biały  (talk) 15:03, 23 February 2011 (UTC)


 * I adjusted the intro according to WP:LEAD. See if you like it. Paolo.dL (talk) 17:13, 23 February 2011 (UTC)

Here are a few more comments, broken up for easier digestion:
 * Ok, the lead looks better now.


 * The references issue is, for me, somewhat minor since WP:SCICITE gives a lot of license to rely on general references for standard material like this. But adding a few more inline citations couldn't hurt (one per section minimum is the general rule of thumb for me if an articles is seeking advancement).


 * The lead image is nice eye-candy, but it seems to me that it would be more informative in the "Intuitive interpretations" section. The caption is too long as well.  If it takes more than a sentence to explain an image, then that means that it is not tied to the text well enough.


 * The article could also use more images in the earlier sections. There are probably only so many ways one can illustrate the SVD, but I'd get creative with some stills as well as the animation.  Can the three-dimensional case be visualized as well?  I learned the SVD first from Gilbert Strang's textbook "Linear algebra and its applications".  If I recall correctly, he has some nice matrix visualizations, and you might consider incorporating something like what he does.


 * It seems to me that the "Geometric meaning" section should be simplified and merged into the "Intuitive interpretations" section.


 * The relationship of singular values to eigenvalues should also be given more emphasis earlier on in the text. Consider simplifying the existing section and moving it up.


 * It also seems to me that a section about how to calculate the SVD "by hand" should be given greater prominence. (This is currently buried in the abstract "Existence" section, more on this below.)


 * I would also consider rewriting the example to show how the singular value decomposition is obtained, not merely that it exists (also a 2x2, 2x3, or 3x3 example should be enough, even if the numbers don't come out so prettily).


 * I would gut the "Existence" section: explain earlier on how to use the spectral decomposition of positive definite matrices to get the SVD (hopefully the treatment can be simplified somewhat, I haven't thought about it), then explain the variational characterization plainly (lose the "theorem-proof" paradigm). Retitle the section "Variational characterization".

Best, Sławomir Biały  (talk) 14:12, 24 February 2011 (UTC)


 * Thank you. This seems to be a precious list of good advices. In my opinion, you should copy it in the talk page. Paolo.dL (talk) 17:10, 24 February 2011 (UTC)