Gauss-Jordan algorithm | Gauss-Jordan elimination method | Gauss-Jordan method

A method for finding a matrix inverse. To apply Gauss-Jordan elimination, operate on a matrix [A | I] congruent [a_11 | ... | a_(1n) | 1 | 0 | ... | 0 a_21 | ... | a_(2n) | 0 | 1 | ... | 0 ⋮ | ⋱ | ⋮ | ⋮ | ⋮ | ⋱ | ⋮ a_(n1) | ... | a_(n n) | 0 | 0 | ... | 1], where I is the identity matrix, and use Gaussian elimination to obtain a matrix of the form [1 | 0 | ... | 0 | b_11 | ... | b_(1n) 0 | 1 | ... | 0 | b_21 | ... | b_(2n) ⋮ | ⋮ | ⋱ | ⋮ | ⋮ | ⋱ | ⋮ 0 | 0 | ... | 1 | b_(n1) | ... | b_(n n)].

condensation | Gaussian elimination | LU decomposition | matrix equation