# Module extendr_api::prelude::modules::cholesky::llt

## Expand description

The Cholesky decomposition of a Hermitian positive definite matrix $A$ is such that: $$A = LL^H,$$ where $L$ is a lower triangular matrix.

## Modules§

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

## Structs§

- This error signifies that the LLT decomposition could not be computed due to the matrix not being numerically positive definite.