An Explicit Construction of Gauss-Jordan Elimination Matrix

Abstract

A constructive approach to get the reduced row echelon form of a given matrix $A$ is presented. It has been shown that after the $k$th step of the Gauss-Jordan procedure, each entry $a_{ij}^k(i<>j;j>k)$ in the new matrix $A^k$ can always be expressed as a ratio of two determinants whose entries are from the original matrix $A$. The new method also gives a more general generalization of Cramer's rule than existing methods.

Cited by in corpus (1)

• The explicit formula for Gauss-Jordan elimination and error analysis