That was a really computation-intensive, brute-force derivation of grad log |det W|.
I know there is a more elegant approach that makes better use of the determinant's core properties, but it's been ages since I saw it.
I know there is a more elegant approach that makes better use of the determinant's core properties, but it's been ages since I saw it.
https://math.stackexchange.com/questions/38701/how-to-calcul...
Though, there are other ways to derive it. My personal opinion is that the vector and matrix calculus derivations in the book are too verbose, but this style may be more comfortable for some readers. My personal opinion is that the semidefinite and cone optimization communities have more concise ways of deriving these kind of derivatives and relationships. For example, this can be seen in Boyd and Vandenberghe's Convex Optimization or Ben-Tal and Nemirovski's Lectures on Modern Convex Optimization.
Brute-forcing it would be to write down the multivariate polynomial in full generality, as there would be no way to break it up using the logarithm.