Triangular factorization and inversion by fast matrix multiplication

Abstract

The fast matrix multiplication algorithm by Strassen is used to obtain the triangular factorization of a permutation of any nonsingular matrix of order n in > C 1 n log 2 7 > {C_1}{n^{{{\log }_2}7}} operations, and, hence, the inverse of any nonsingular matrix in > C 2 n log 2 7 > {C_2}{n^{{{\log }_2}7}} operations.