I am learning about Hermitian positive definite matrices and the way that they can be decomposed with Cholesky decomposition. I have learned that these matrices deserve special attention for how often they are used when dealing with numerical linear algebra.
My question is simply: what (real-world) applications are there that use Hermitian positive definite matrices? For example, in statistics the covariance matrix of a multi-variate probability distribution is positive semi-definite. I am also inclined to think that positive definite matrices occur in finite-difference methods of solving PDEs. What other applications of such matrices are there? All thoughts are welcome and examples/sources are greatly appreciated!