I am reading through this paper to try and code the model myself. The specifics of the paper don't matter, however in the authors matlab code I noticed they use a Cholesky decomposition instead of computing the determinant of a covariance matrix directly.
Specifically, the author has
$$\log\det(\Sigma) = 2 \sum_i \log [ diag(L)_i ]$$
where $L$ is the lower triangular matrix produced by a Cholesky decomposition of the covariance $\Sigma$.
I tested this out myself using various covariance matrices and found the relation above always works to within 14 decimal places (it's probably just a machine precision issue). I believe the author uses a cholesky decomposition because it is slightly faster to compute than computing the determinant directly (at least when I timed it on my machine).
My question is, why does this relation hold true? I couldn't find any references in the paper / code, or any material online.