# 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

## 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}` |