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 of invertible matrices. Left multiplication (pre-multiplication) by an elementary matrix represents elementary row operations, while right multiplication (post-multiplication) represents elementary column operations. The acronym "ERO" is commonly used for "elementary row 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.
In algebraic K-theory, "elementary matrices" refers only to the row-addition matrices.
Read more about Elementary Matrix: Operations
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