Gauss-Jordan Elimination

A method for finding a matrix inverse. To apply Gauss-Jordan elimination, operate on a matrix

(1)

where  is the identity matrix, and use Gaussian elimination to obtain a matrix of the form

(2)

The matrix

(3)

is then the matrix inverse of . The procedure is numerically unstable unless pivoting (exchanging rows and columns as appropriate) is used. Picking the largest available element as the pivot is usually a good choice.