Elementary Matrix - Wikipedia - en.wikipedia.org ![rw-book-cover|200x400](https://readwise-assets.s3.amazonaws.com/static/images/article2.74d541386bbf.png) ## Metadata - Author: **en.wikipedia.org** - Full Title: Elementary Matrix - Wikipedia - Category: #articles - Tags: #mathematic - URL: https://en.wikipedia.org/wiki/Elementary_matrix ## Highlights - In mathematics, an elementary matrix is a matrix which differs from the identity matrix by one single elementary row operation. The elementary matrices generate the general linear group GLn(F) when F is a field. Left multiplication (pre-multiplication) by an elementary matrix represents elementary row operations, while right multiplication (post-multiplication) represents elementary column operations. Elementary row operations are used in Gaussian elimination to reduce a matrix to row echelon form. They are also used in Gauss–Jordan elimination to further reduce the matrix to reduced row echelon form.