# Cholesky factorization

Given an $LaTeX: m \times m$ symmetric matrix $LaTeX: A$, a lower triangular matrix, $LaTeX: L$, is obtained, called the Cholesky factor, such that $LaTeX: A = LL^T$. This is particularly useful for solving linear systems, $LaTeX: Ax=b$, by using forward substitution, $LaTeX: Ly=b$, then backward substitution, $LaTeX: L^T x = y$. The original algorithm assumes $LaTeX: A$ is positive definite, but it can apply more generally. This is also called Cholesky decomposition.