I was asked to find the Hessian of the following function:
$$ f(X,Y) = \frac{1}{2}|| M - XY^T||_F^2$$ where $X$ is a $m \times r$ matrix and $Y$ is a $n \times r$ function.
$||z||_F$ is defined for an $ l \times k$ matrix as:
$$ ||z||_F = \sqrt {\sum_{i=1}^l \sum_{j=1}^k Z_{ij}^2}$$
It's a part of an exercise from some course that I haven't covered. I haven't found any resources that helps me to solve this problem. Any help, references will be greatly appreciated.