Hands-On Mathematics for Deep Learning

Cholesky decomposition

As I'm sure you've figured out by now, there is more than one way to factorize a matrix, and there are special methods for special matrices.

The Cholesky decomposition is square root-like and works only on symmetric positive definite matrices.

This works by factorizing A into the form LL^T. Here, L, as before, is a lower triangular matrix.

Do develop some intuition. It looks like this:

However, here, L is called a Cholesky factor.

Let's take a look at the case where .

We know from the preceding matrix that ; therefore, ...