Talk:Main diagonal

Notation

Is there a standard notation for the main diagonal of matrix M? Do people say $diag(M)$ or something? --Doradus (talk) 15:35, 2 September 2009 (UTC)[reply]

I don't know of any. Scientific29 (talk) 10:07, 12 April 2014 (UTC)[reply]

I don't think so, I guess you'd simply write D = ( A_ij delta_ij)_ij . In any case, diag(x) would usually mean D = ( x_i delta_ij )_ij, that is, x is a vector that holds the elements of the diagonal which are the only nonero elements of D. — MFH:Talk 13:32, 10 July 2024 (UTC)[reply]

Inadequate reference

The article says, "In linear algebra, the main diagonal (sometimes principal diagonal, primary diagonal, leading diagonal, or major diagonal) of a matrix {\displaystyle A} A is the collection of entries {\displaystyle A_{i,j}} A_{i,j} where {\displaystyle i=j} i=j." It also shows non-square matrices and indicates a main diagonal in them in red.

https://wikimedia.org/api/rest_v1/media/math/render/svg/9224f95b8332a444021043d15593c5e41e4321fd

But the reference (http://mathworld.wolfram.com/Diagonal.html) specifically mentions that the main diagonal exists in a SQUARE matrix. It does not, however, say that a main diagonal cannot exist in non-square matrices. Where is the reference that mentions that leading diagonals can be present in non-square matrices? — Preceding unsigned comment added by Oitijhya (talk • contribs) 11:58, 19 May 2018 (UTC)[reply]

This article is in dire need of other references. I wouldn't call MathWorld a "reliable source". Especially for the names of the diagonal and antidiagonal: some user came up with "Harrison diagonal," which is nowhere to be found on Google, and their claim stood up for half a year. – OfficialURL (talk) 07:44, 1 December 2021 (UTC)[reply]

what about to next-to-main diagonal ?

I'm not sure "secondary" is a universally accepted term for the "anti-diagonal(s)".
I do think that "anti-diagonal" (with or without "-") is a standard term for diagonals that run from SW (lower left) to NE (upper right) ("raising anti-diagonals") or the opposite sense ("falling anti-diagonals"), possibly not only the main anti-diagonal (for a matrix of size N x N that would be (A_{i,N+1-i})_{i=1..N} but also secondary anti-diagonals (as I would call them) of the form A_{i,k-i} {i=1..k-1} for k different from N+1).
But without "anti", I think "secondary (or: non-principal) diagonal(s)" often mean the diagonals next or parallel to the main diagonal, viz, A_{i,i+-1} {i=1..N-1}, etc. (Maybe "k-th secondary diagonals" for A_{i,i+-k} {i=1..N-k}, k = 1, 2, 3...?)
Or otherwise, how would you call these? — MFH:Talk 13:44, 10 July 2024 (UTC)[reply]