# Module extendr_api::prelude::modules::cholesky::ldlt_diagonal

## Expand description

The Cholesky decomposition with diagonal $D$ of a Hermitian matrix $A$ is such that: $$A = LDL^H,$$ where $D$ is a diagonal matrix, and $L$ is a unit lower triangular matrix.

The Cholesky decomposition with diagonal may have poor numerical stability properties when used
with non positive definite matrices. In the general case, it is recommended to first permute
(and conjugate when necessary) the rows and columns of the matrix using the permutation obtained
from `faer::linalg::cholesky::compute_cholesky_permutation`

.

## Modulesยง

- Computing the decomposition.
- Solving a linear system using the decomposition.
- Updating the decomposition.