Matrix factorization (or matrix decomposition) is a product of an input matrix A so that

                A = F_1F_2...F_k.
            
Matrix factorization is a base technique for implementing matrix algorithms, including solving a system of linear equations. In LAPACK, routines that perform matrix factoring are in the form of xyyTRF.

The method of the factorization depends on the properties of the matrix A. The main types of factorizations in LAPACK for solving a system of linear equations are:

whiere L is lower triangular, U is upper triangular, and P is a permutation matrix.