I have a machine learning regression problem. I need to minimize
However I am trying to find matrix $A$, not the usual $x$, and I have lots of example data for $x_i$ and $b_i$. In general $A$ has more rows than columns.
Additionally I would like a solution for minimizing the Mahalanobis distance version, where $C$ is the SPSD covariance matrix:
I'm thinking that my problem can be re-written into the usual least squares problem but not sure if I am doing it correctly.