Study on Matrix Inverse as by-Product of Determinant

Abstract

The determinant of a given square matrix is obtained as the product of pivot elements evaluated via the iterative matrix order condensation. It follows as the by-product that the inverse of this matrix is then evaluated via the iterative matrix order expansion. The fast and straightforward basic iterative procedure involves only simple elementary arithmetical operations without any high mathematical process. Remarkably, the revised optimal iterative process will compute without failing the inverse of any square matrix within minutes, be it real or complex, singular or nonsingular, and amazingly enough even for size as huge as 999x999. The manually extended iteration process is also developed to shorten the iteration steps, if the calculation of small size inverse matrices is feasible.