Definition
Plain language
A small matrix calculation used to solve certain equations efficiently.
As stated in the literature
A decomposition of a symmetric positive-definite matrix into a triangular factor and its transpose, used to solve linear systems quickly.
Why it matters: It's a workhorse subroutine that makes many statistical and optimization methods practical at scale.
For example, in a Gaussian process regression, Cholesky factorization is used to invert the covariance matrix and produce predictions in a numerically stable way.
Heard on the show
“The closed-form solve requires a small Cholesky factorization at query time.”Episode 033 — Echo: The Paper Arguing You Never Needed a KV Cache for Retrieval