Talk:Matrix of ones

identity matrix

For me a unit matrix is completely synonymous with an identity matrix. When I saw this article I checked some books from my bookcase and found that I am not alone in this. I gave 5 references to support my view, but could have given 25 as easily. Doing this check I did not find any support for the present definition (a matrix with 1s everywhere). Even my (German) edition of Gantmacher doesn't give it, Gantmacher gives Einheitsmatrix, (lit. unit matrix), though, for the identity matrix. So, please support the present definition with a few sources.--P.wormer 10:57, 21 June 2007 (UTC)[reply]

I am neither familiar with the term, and I do not know if it is standard. However, note that "identity matrix" depends on how matrix multiplication is defined. The identity matrix (with 1:s on the diagonal) is related to the "usual" matrix multiplication. However, there are also other ways to multiply matrices. One is the Hadamard product. In this product, the identity operator is represented by the "unit matrix". I added a very short note in the entry about this. In Matlab the "unit matrix" can be created with the command ones(n,n), so I think the entry is merited, although the current title is misleading. Haseldon 13:38, 21 June 2007 (UTC)[reply]

Exactly, that is what I suspected: the present definition of unit matrix is inspired by the command ones(n,m) of Matlab. In computer programming a matrix with the number 1 everywhere can be handy, especially in Matlab's pointwise (Schur, Hadamard) product, but in vector space oriented mathematics there is hardly a need for such a matrix. So, the question remains how widespread the term "unit matrix" is (in the definition of the present article).--P.wormer 15:25, 21 June 2007 (UTC)[reply]

PS1 The help of Matlab says: "ONES(M,N) is an M-by-N matrix of ones." (and does not use the term "unit matrix").--P.wormer 16:59, 21 June 2007 (UTC)[reply]

PS2 I did a Google search on unit matrix, and except for this article, I did not find elsewhere the meaning "matrix with ones" (but very often I did find identity matrix). This meaning to the term was given by Peskydan, who seems to have left Wikipedia. I'm inclined to think that the term is an idiosyncracy of Peskydan.--P.wormer 17:20, 21 June 2007 (UTC)[reply]

I also searched Amazon for unit matrix, and I was not able to find justification for the name of this entry. I think a suitable name would be 'ones-matrix' (9290 Google hits) or "all-ones matrix" (557 Google hits). Haseldon 19:23, 21 June 2007 (UTC)[reply]

How about 'matrix of ones'? --HappyCamper 21:33, 21 June 2007 (UTC)[reply]

Even better. 'matrix of ones' has 24500 Google hits. However, as all of these terms are in use, they should probably all have redirects. Haseldon 22:16, 21 June 2007 (UTC)[reply]

I agree. Also, this "unit matrix" article should redirect to "identity matrix". If all is well, I'll make the changes tomorrow. Sound good? --HappyCamper 00:29, 22 June 2007 (UTC)[reply]

Certainly. Haseldon 07:54, 22 June 2007 (UTC)[reply]

HC wrote: I agree. Also, this "unit matrix" article should redirect to "identity matrix" [..] I'll make the changes tomorrow. This completes the circle, for Peskydan wrote regarding the same redirect: This went unchecked for 2 years! Unit matrix is rarely used to mean identity. I'll mend all pages linking here immediately. This reminds me of sisyphus' boulder : - ( In addition this casus illustrates a danger inherent to Wikipedia. A sole editor introduces something (s)he believes to be correct, other Wikipedians accept it and via Google it becomes a world-wide standard. It would have been very annoying if the Wikipedia definition of "unit matrix" had remained solely that of "matrix of ones", because whatever present usage of the term "unit matrix", there is a vast literature out there in which "unit" and "identity" matrix are identical and Wikipedia should mention that. The list of references in the present article can go now, because none of it mentions "matrix of ones". I entered the references to prove my point, believing Peskydan that in some field beyond my horizon (articial intelligence perhaps?) the usage of the term would be different. --P.wormer 08:28, 22 June 2007 (UTC)[reply]

(de-indenting) I have a vague recollection that I looked into it some years ago and that I did find some instances where "unit matrix" means a matrix of ones. However, I'm not sure, the vast majority used it in the meaning of "identity matrix" (which is also the only meaning I've seen in papers I've actually read), and I don't care enough to redo the search. So I agree with the change. -- Jitse Niesen (talk) 09:18, 22 June 2007 (UTC)[reply]

See Mathematica for the usage of "unit matrix" for "matrix of ones". Maybe we were too quick? Should this (very unfortunate) alternative usage not be mentioned? I entered a sentence in the manner of dr. Johnson giving a personal opinion on its use.--P.wormer 07:48, 23 June 2007 (UTC)[reply]

Hmm...I think it should be mentioned, but just briefly. I made the mentioning of it even shorter than before. What do you think? I'll make a note to find some book references to to this the next time I visit the library. --HappyCamper 15:31, 23 June 2007 (UTC)[reply]

Trace of J

Why refer to Stanley's book on Algebraic Combinatorics for the totally obvious fact that the trace of an all-ones, $n\times n$ matrix is $n$ ? Turgidson (talk) 22:27, 22 June 2018 (UTC)[reply]

We are using the Stanley reference anyway for the eigenvalues, so it does no harm to use the same reference for the trace. And although I agree that this one is pretty obvious and trivial, what may seem a routine calculation to some editors or readers may be difficult for others. —David Eppstein (talk) 22:47, 22 June 2018 (UTC)[reply]

OK, I guess, but don't all these assertions (i.e., points 2 and 3 from that list) follow at once from the computation of the characteristic polynomial (i.e., point 1 from the list), which itself is given without any reference? Perhaps reference should be given to point 1 (although that's also an exercise), and then state that points 2 and 3 follow from that? Just a thought... Turgidson (talk) 15:28, 23 June 2018 (UTC)[reply]

Generalize the matrix exponential

I suggest to generalize the expression of the matrix exponential of an all-ones matrix by including a generic constant $\mu$ :

$\exp(\mu J)=I+{\frac {e^{\mu n}-1}{n}}J$ Paolostar (talk) 11:47, 26 June 2024 (UTC)[reply]