Inverse and Determinant of a Square Matrix by Order Expansion and Condensation [EM Programmer's Notebook

Abstract

A simple and straightforward fast iterative method is presented for computing the inverse and determinant of any square matrix by successively applying order condensation and order expansion in an iterative process. Applying the optimal iteration process, which comprises only some 20 lines of the MATLAB source code (using only simple elementary arithmetical operations), the inverse matrix can be computed within minutes from any given square matrix, even of relatively large size (such as 999), with real or complex entries, and irrespective of whether the matrix is singular or nonsingular.