Gauss–Jordan elimination

Gauss–Jordan elimination is a version of Gaussian elimination that puts zeros both above and below each pivot element as it goes from the top row of the given matrix to the bottom. Gauss–Jordan elimination is considerably less efficient than Gaussian elimination with backsubstitution when solving a system of linear equations. However, it is well suited for calculating the matrix inverse. Every matrix has a reduced row echelon form, and both algorithms are guaranteed to produce it.

It is named after Carl Friedrich Gauss and Wilhelm Jordan, because it is a modification of Gaussian elimination as described by Jordan in 1887. However, the method also appears in an article by Clasen published in the same year. Jordan and Clasen probably discovered Gauss–Jordan elimination independently.[1]

In computer science, Gauss-Jordan elimination as an algorithm has a time complexity of O(n3