Talk:Elementary matrix

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 Field: Algebra


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

Alternate meaning[edit]

Doesn't "elementary matrix" also refer to a matrix E_{ij} consisting of a single entry 1, and the rest 0? (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. (talk) 16:04, 27 February 2011 (UTC)

What is the correspondence? Multiplication from the left.[edit]

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[edit]

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? (talk) 21:17, 27 February 2013 (UTC)