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.
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.