A Gauss-Jordan matrix is a matrix associated with Gauss-Jordan elimination, but the term has more than one usage. An elementary Gauss-Jordan matrix is an elementary matrix obtained by performing one elementary row operation on the identity matrix. Left multiplication by it performs that row operation (Achar 2000).
The term is also used for a matrix in reduced row echelon form, the final form produced by Gauss-Jordan elimination. This usage distinguishes the reduced matrix from the elementary matrices used to obtain it.
