---
date: '2024-10-28'
description: decomposition of hermitian positive-definite matrices into lower triangular form and conjugate transpose, used for monte carlo simulations.
id: Cholesky decomposition
modified: 2026-06-05 15:08:06 GMT-04:00
tags:
  - math
title: Cholesky decomposition
created: '2024-10-28'
published: '2024-10-28'
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slug: thoughts/Cholesky-decomposition
permalink: https://aarnphm.xyz/thoughts/Cholesky-decomposition.md
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---
decomposition of a Hermitian, positive-definite matrix into the product of a lower triangular matrix and its conjugate transpose. (used for [[thoughts/Monte-Carlo#simulations|Monte-Carlo simulations]])

$$
A = LL^{*}
$$

where $L$ is a lower triangular matrix with real and positive diagonal entries, and $L^{*}$ is the conjugate transpose of $L$.