Of course everyone in the Bsky community knows all these results off the top of their head. But in case you have colleagues or students who may not I thought I'd share. www.sciencedirect.com/science/arti...
This brings back fond memories. I remember using results by Magnus & Neudecker in my thesis - Magnus,J.R. and Neudeucker,H. (1979). The commutation matrix: some properties and applications. Ann. Statist.,7,381-394. projecteuclid.org/journals/ann...
The commutation matrix $K$ is defined as a square matrix containing only zeroes and ones. Its main properties are that it transforms vecA into vecA', and that it reverses the order of a Kronecker prod...
Now we just need to get a really good explainer on tensors into the hands of all the baby AI engineers cluttering up arXiv with error-ridden tensor math statements in their attempts to describe or analyze their models.
A gentle trip down memory lane; a steep learning curve, employed in three metrics courses in the PhD program: basics, taught by Erwin Charlier, financial, by Bas Werker, and panel, by Arthur van Soest