Talk:Elementary matrix

Lock

Why is this article locked? — Preceding unsigned comment added by 128.220.31.54 (talk) 19:34, 29 June 2011 (UTC)

Alternate meaning

Doesn't "elementary matrix" also refer to a matrix E_{ij} consisting of a single entry 1, and the rest 0? 76.126.116.54 (talk) 08:28, 12 December 2008 (UTC)

Dummit and Foote's Abstract Algebra (3rd Ed.) uses the notation $E_{ij}$ as you suggest, but only in an exercise (7.2.6). It doesn't give a name to those matrices, either. It uses them later in exercise 7.3.21 to show that any two-sided ideal of $M_{n}(R)$ is $M_{n}(J)$ for a two-sided ideal J of R, but the matrices themselves don't seem terribly important. 67.158.43.41 (talk) 16:04, 27 February 2011 (UTC)

What is the correspondence? Multiplication from the left.

The article says that the elementary matrices correspond to the elementary row operations but does not mention that if you have any elementary matrix E and take any matrix M with the same number of rows as the number of columns of E, then E*M gives a matrix which has the elementary operation of E performed on the rows of M. To see this, extend the columns of M by an identity matrix with the same number of columns as the number of rows of M. See, e.g. Cliff's notes on this subject Penguian (talk) 00:16, 6 September 2010 (UTC)

You're correct; I've now made this change. Next time, instead of letting it sit for two years, be bold and improve it yourself! :-) Mark M (talk) 17:13, 29 November 2012 (UTC)

Row addition

The article says that for row addition i must not be equal to j. But if it is, the operation would be simply multiplying that row by k+1. Swapping two rows can also be done by a series of row additions. So these could be considered special cases rather than different operations. Should this be mentioned in the article? 85.181.190.22 (talk) 21:17, 27 February 2013 (UTC)

Elimination Matrices

https://ocw.mit.edu/courses/mathematics/18-06sc-linear-algebra-fall-2011/ax-b-and-the-four-subspaces/elimination-with-matrices/MIT18_06SCF11_Ses1.2sum.pdf Elimination matrices sounds similar enough to what is in here to possibly merit a mention I think. HoboMcJoe (talk) 03:29, 19 October 2016 (UTC)

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It may need to clarify that multiplication of an elementary matrix to any matrix results in the corresponding elementary row operation on the matrix.

Hi.

In the introductory section, there are the below sentence.

"Left multiplication (pre-multiplication) by an elementary matrix represents elementary row operations, while right multiplication (post-multiplication) represents elementary column operations."

I think it needs to be changed to the following. The difference is only that plural words "operations" are changed to singular words "operation", and the reason of such suggested change is that multiplication of an elementary matrix results in the corresponding single row or column operation, not compound operations.

"Left multiplication (pre-multiplication) by an elementary matrix represents the corresponding elementary row operation, while right multiplication (post-multiplication) represents the corresponding elementary column operation." Goodphy (talk) 03:40, 17 September 2025 (UTC)

Agree. Tito Omburo (talk) 12:21, 17 September 2025 (UTC)

Thank you for your quick response, and I have made this change on this article. Goodphy (talk) 03:55, 18 September 2025 (UTC)