Primary
Elementary Matrix ○꠹｜Definition｜1st｜20260604202716-00-⌔
Elementary matrix
In mathematics, an elementary matrix is a square matrix obtained from the application of a single elementary row operation to the identity matrix. The elementary matrices generate the general linear group GL (F) when F is a field. 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.
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.
Printed 2026-06-28.
(echo:: @ ᯤ)
Link to original
Secondary
• • •