I've got an expression like:
$\frac{\partial}{\partial A} \text{Tr}\left(\wedge^k \sum_{t=1}^T A^t(B^t)^T\right)$
where $A, B$ are linear operators (matrices).
How would I go about computing this derivative? I believe, if the summand is a vector instead, the expression would reduce to
$ \frac{\partial}{\partial v} \text{det}\begin{pmatrix}\text{something}\end{pmatrix} $
But I'm not too familiar with exterior algebra, and in particular, I'd love some guidance on the output type of the value within the $\text{Tr}(\ )$. Is it some kind of a signed volume? If so, what is the trace of that?
I'm happy to see an example for even just the $k=2$ case.