# Module full_pivoting

## Expand description

The full pivoting LU decomposition is such that: $$PAQ^\top = LU,$$ where $P$ and $Q$ are permutation matrices, $L$ is a unit lower triangular matrix, and $U$ is an upper triangular matrix.

The full pivoting LU decomposition is more numerically stable than the one with partial pivoting, but is more expensive to compute.

## Modulesยง

- Computing the decomposition.
- Reconstructing the inverse of the original matrix from the decomposition.
- Reconstructing the inverse of the original matrix from the decomposition.
- Solving a linear system using the decomposition.