LU decomposition LU decomposition or LU factorization of a square matrix is a factorization of as the product of two matrices and : , where is a lower-triangular matrix and is an upper-triangular matrix. Syntax lu_decomposition(Matrix) Description lu_decomposition(Matrix) Given a matrix, returns a list with the matrices and . If the permutation matrix is different of the identity matrix or the option permutation_matrix is set to 1, the permutation matrix is returned at the first position. Options Below is a complete list of options that may be used in the lu_decomposition function. Option Description Format Default value permutation_matrix We can choose if the permutation matrix is showed or not. When the value equals 0, the permutation matrix is returned if and only if it is different from the identity matrix. If it is set to 1, the permutation matrix is returned always. If it is set to -1, the permutation matrix is not returned. {permutation_matrix=-1} {permutation_matrix=0} Related functions Eigenvalues and eigenvectors, QR decomposition Table of Contents Syntax Description Options Related functions