# Matrix Factorizations

In some applications, you may only want to factor the n × n matrix A into a product of two triangular matrices. Functions and procedures that end with “FAC” are designed to compute these factorizations. Suppose that in addition to the solution x of a linear system of equations Ax = b, you want the LU factorization of A. First, use the IMSL_LUFAC procedure to obtain the LU factorization in a condensed format, then call IMSL_LUSOL with this factorization and a right-hand side b to compute the solution. If the factorization is desired in separate, full matrices, call the IMSL_LUFAC procedure with the keywords L and U to return L and U separately.

Besides the basic matrix factorizations, such as LU and LLT, additional matrix factorizations also are provided. For a real matrix A, QR factorization can be computed by the IMSL_QRFAC procedure. Functions for computing the Singular Value Decomposition (SVD) of a matrix are discussed in “Singular Value Decomposition and Generalized Inverse”.