Not really the covariance matrix, though, but its Cholesky decomposition (which exists, as a covariance matrix is symmetric positive (semi)definite, as otherwis

Not really the covariance matrix, though, but its Cholesky decomposition (which exists, as a covariance matrix is symmetric positive (semi)definite, as otherwise you could construct a linear combination with negative variance). Useful stuff. And vice versa, btw - take iid RV with unit variance, hit them with the Cholesky decomposition, and you have the desired covariance. Used all over Monte Carlo and finance and so on.