Introduction

Introduction

For positive numbers we can take square roots: $9 = 3\cdot3$. Symmetric positive definite matrices have an equivalent — the Cholesky decomposition $A = LL^\top$, with $L$ lower triangular. It is about twice as fast as general elimination and is the standard way to work with covariance matrices: sampling from Gaussians, computing log-determinants, and solving systems in Gaussian processes.