I am looking for a way to determine a complex matrix $C \in \mathbb{C}^{n\times m}$, $m\leq n$ such that
$$||AC-\mathbf{I}_m||_{\rm F}^2$$
gets minimized, where $\mathbf{I}_m$ is the $m$-dimensional identity matrix, $||\cdot ||_{\rm F}$ is the Frobenius-norm and $A\in\mathbb{C}^{m\times n}$ is known. In principle there are no further assumptions made to the matrices $A$ and $C$. I have already figured out that a SVD and the low-rank approximation may be some clues for solving that problem, but I did not manage to apply this to my specific problem. Would it be helpful to choose $C$ to be the pseudo-inverse of $A$? I'd be grateful for all helpful advices or even solutions!
Best Answer
Considering the definition of the pseudoinverse I think you have already answered your question.