Suppose that I have two real-valued matrices $\bf{A}$ and $\bf{B}$. Both matrices are exactly the same size. I multiply both matrices together in a point-by-point fashion similar to the Matlab A .* B
operation.
Under what conditions can I approximately separate $\bf{A}$ and $\bf{B}$ using Principle Components Analysis (PCA)? Would it be possible to remove some components of the product A .* B
to get an approximation of $\bf{A}$ or $\bf{B}$?
What algorithm might be best suited for this operation?
I am not looking for an exact separation of the matrices, but a separation using some sort of (statistical or numerical?) constraints. How would I set this problem up, and is there a good example of how to do this?