Talk:List of matrices

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let's have more than a dumb list

a little on what these are & why they are interesting. Examples would be even better, but I suspect TeX in a list will look lousy -- Tarquin 11:26 Mar 9, 2003 (UTC)


I am looking for

the name of a 0-1 matrix A with the specification: where iterates over the rows and over the columns. The matrix has 1s around the main diagonal and 0s in the LL and UR corners, yet the tube of ones does not have to be as regular as in e.g. a tridiagonal 0-1 matrix. Can anybody help me? --Johannes Hüsing 13:35, 2 Feb 2005 (UTC)

Change in layout

I've added quite a few new matrices and matrix descriptions over the past few days, but during the process it became clear that there is still a lot of cleanup required here. There are effectively duplicates still in the list - e.g. transition matrix and stochastic matrix link to the same thing. (I'm not sure they actually are the same thing - isn't a stochastic matrix a particular type of transition matrix? I think Michael Hardy might be helpful here!) Duplicates are not a bad thing - but they need to be marked up as such. Also there are still a few matrices without descriptions.

The other thing I've done is to separate out the non-matrices, e.g. Wronskian, "Row echelon form" etc, as these aren't strictly matrices so didn't seem appropriate to the list. It may be worthwhile reconsidering this document more as a matrix/linear algebra glossary - in which case it would be well worthwhile expanding the "other matrix terms" section I added at the end.

Hopefully this helps take things a little farther toward Tarquin's vision of "more than a dumb list". I also hope that nobody feels their toes have been stepped on!

Dan Pope 20:05, 6 November 2006 (UTC)

I've just finished the matrix descriptions, and moved 'overlap matrix' to the science/engineering section. However, I'm not convinced that overlap matrices are used only in this context - they look too fundamental, and potentially very useful for a wide range of applications. If anyone has any knowledge of this, please alter the link, description and/or "overlap matrix" article if necessary! Dan Pope 21:02, 6 November 2006 (UTC)

Further division?

I'm very tempted to further divide this list - there are some really fundamentally important matrices, and many less important or very specialist matrices, lumped together indiscriminately. Might a "fundamental/basic matrices" or similarly titled section preceding the rest of the maths matrices, perhaps help people find what they need? Things like the identity matrix, Hermitian matrix, symmetric matrix, etc. Any thoughts? Dan Pope 21:24, 6 November 2006 (UTC)

I support that idea. (BTW: The list is already divided.) Here are possible new subsections:
Standards: identity matrix, zero matrix.
Specific matrices: These only depend on their dimension: like the Hilbert matrix, identity matrix, and exchange matrix.
Vector spaces of matrices: symmetric, antisymmetric, and diagonal matrices.
Haseldon 22:18, 19 November 2006 (UTC)
The idea of subdividing the list is good. I think the main use for the list is when you are looking for the name associated with a certain property (e.g., how do you call a matrix satisfying ). The problem is how to subdivide. Dan Pope's idea is good in principle, but it may be hard to decide which matrices are deemed basic. Splitting off "specific matrices", as Haseldon proposes, seems good. I'm more sceptical about "vector spaces of matrices", but there is a need for a category with symmetric, antisymmetric, diagonal matrices etc and I can't think of a better name.
How about listing matrices according to application (matrices in statistics, matrices in graph theory), similar to what we're doing now with matrices for phyisics? -- Jitse Niesen (talk) 01:31, 20 November 2006 (UTC)
I agree that further subdivision of this list is a good idea. We now have categories for alphabetical lists. The tricky part is the appropriate subdivisions. I would avoid a basic or fundamental category. As Jitse suggests, I think application specific subdivision is good. Other possible categories:
  • Matrices with special symmetries: symmetric, antisymmetric, Hermitian, etc.
  • Matrices with algebraic properties: zero, identity, inverse, idempotent, etc.
  • Matrices with special structure: block, band, diagonal, tridiagonal, block diagonal, etc.
If some minor overlap occurs, I don't think its a big deal. --Fropuff 02:17, 20 November 2006 (UTC)

Good suggestions. When I originally divided the list, I was sorely tempted to go further, with sections such as "Matrices in statistics"; the problem comes when deciding which section is more appropriate - it's by no means obvious for some matrices which have major application in more than one field. The "fundamental matrices" idea was simply a starting point; I deferred the edit simply because it's not a well defined title as Jitse rightly points out. We might do well to make a list of suggested matrix-section memberships. Accordingly, I've made a page we can update and play with here.

Forgive the excessive length of this!! There are a few other things worth mentioning. Firstly, the dash character separating names from descriptions is not the usual hyphen character -, rather it is — (the 'em dash'). This looks better, and I have carried on using it when adding matrices. However, it isn't sufficiently obvious to those who haven't edited this article much (as is apparent if you look down the list - I've had to correct inconsistencies several times) so I'm going to replace all instances of it with —. This may seem heavy-handed, but it does then become clear to editors not to use the hyphen character. Secondly, the em-dash is not strictly part of the standard ASCII character set; it appears in the Windows Central Europe and 'Western' encodings but is assigned a different character code in other encodings (Hebrew, Baltic, etc) and may not appear correctly on all systems. The MediaWiki engine automatically converts — into a suitable unicode character, so it should be the way to go.

We also need to decide on a few other consistency-related things. I've added about 40 matrices and descriptions to the list so far, and have only wiki-linked the names of matrices in the descriptions when they are quite specific. In "Block-diagonal matrix — a block matrix with entries only on the diagonal", it seems redundant to link block matrix, especially since its entry appears on the following line. Linking all the terms seems to reduce the clarity of the list, and draws attention away from the primary purpose of the document, especially since such entries should be in the list anyway, and linking directly loses the concise descriptions that are often all that the user is looking for. Furthermore, the swathe of blue on the left serves nicely to separate the terms and descriptions, and the Wikipedia style tends to be to link terms once and once only.

Finally (!!!), again relating to consistency - there are a fair number of matrices with several names. I think ideally we should include all, along with descriptions simply stating "another name for a skew-symmetric matrix" or similar. When someone has heard of a matrix but doesn't remember its exact name, confusion can arise if the name they heard is absent, and a similar one isn't - e.g. if only one of "Hessian" and "Hessenberg" were included due to a different choice of duplicate name, then a reader might find the remaining name sufficiently similar that they might erroneously think they've found what they were looking for.

I've also added links here to the "Matrix theory" and "Matrix (mathematics)" articles. I think this article is a very underrated resource, and once complete could be very useful to a fair number of people.

Dan Pope 03:36, 21 November 2006 (UTC)

Ok, I was stupid. Editing the thing with — everywhere is *horrible*! Instead I've put a comment at the top explaining to editors how to get the correct type of dash. Also, I failed to notice until now that there is an "Insert" link with it on the edit page anyway! Humble apologies... Dan Pope 03:44, 21 November 2006 (UTC)

Alternate sorting

I think it would be useful to have these sorted by property. For example, banded, block diagonal, etc. are all related to matrix shape, a bunch of others have to do with spectral properties. I'm tempted to add a little * to some with a note at the bottom saying these are shape-related properties. Alternately, this could be done using MediaWiki Categories. Thoughts? —Ben FrantzDale 18:43, 20 December 2006 (UTC)

Definition of positive-definite matrix is incorrect

It should not be defined by its eigenvalues but by the following formula (valid for real matrices): A square (n, n) matrix A is positive definite if for each non-zero n-vector x: xTAx > 0.

Unlisted matrix type

Include the name of a matrix of the following form:

  M(i,j)= f(i) g(j),


where f and g are functions of i and j. —Preceding unsigned comment added by Bochovee (talkcontribs) 00:28, 8 December 2007 (UTC)

I'd just call that the outer product (or tensor product) of f(i) and g(i). —Ben FrantzDale (talk) 14:15, 15 January 2010 (UTC)
Or equivalently, a matrix of rank one.–Jérôme (talk) 13:07, 6 May 2012 (UTC)

Quasitriangular matrix

MATLAB mentions the term 'quasitriangular matrix', but I can't find a definition. Should it be in this list? --213.170.45.3 (talk) 17:53, 28 February 2008 (UTC)

Non-mathematical article title

The "List of matrices" is uncountable unless the ground ring in question is countable. There's nothing wrong with the idea for this page but it should be called "List of matrix 'types" or something similar. Sympleko (Συμπλεκω) 19:38, 5 May 2008 (UTC)

Examples in page?

I have been trying to find out if a particular matrix that I need to find the inverse is a type that is well known to mathematicians. This article is a useful collection of the various types of "standard" matrices, but I was wondering if it would be a good idea to show a small example of each kind of matrix in the page itself. This way, someone could scroll down the page to see if there was anything that looked like the thing they were after.

I realise, of course, that this will make things rather longer than they are now, and possibly cluttered, too, so this idea may not be all that great. But perhaps there is some other way in which there could be a "gazetteer" of special matrices that one could cast one's eye down? MarkHudson (talk) 10:52, 19 June 2008 (UTC)


Table Edit

In the table, it's mostly alphabetical, but I is after H, unlike in the table, may want to fix that one, interger after all H... matrices. —Preceding unsigned comment added by 68.101.78.25 (talk) 01:08, 4 June 2010 (UTC)

New edit (russian)

I am russian editor. I am going to edit some articles concern with matrix theory (in ruussian). I'll try to make it better. But... it would be better that the corresponding articles via interwiki are the same contetnt. That's why I am going to edit some articles concern with matrix theory in EnWiki. What shal I do to do it successfull? P.S. My english language is vary bad. But I hope to speak and write fluently. ;-) OZH (talk) 12:09, 17 September 2010 (UTC)