Triangular Factorization and Inversion by Fast Matrix Multiplication

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 $< {C_1}{n^{{{\log }_2}7}}$ operations, and, hence, the inverse of any nonsingular matrix in $< {C_2}{n^{{{\log }_2}7}}$ operations.