How do you solve log determinant? - Answers

To solve for the log determinant of a matrix, you typically compute the determinant first and then take the logarithm of that value. For a positive definite matrix ( A ), the log determinant can be expressed as ( \log(\det(A)) ). If ( A ) is decomposed using methods like Cholesky decomposition, you can simplify the computation by calculating the determinant of the triangular matrix and then applying the logarithm. Additionally, in some contexts, such as with Gaussian distributions, the log determinant can be efficiently computed using properties of matrix trace and eigenvalues.