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In this paper,we study the constrained matrix approximation problem in theFrobenius norm by using the core inverse:\begin{align}\nonumber \left\|{Mx - b}\right\|_F=\min\ \ {\rm subject\ to} \ \ {x\in\mathcal{R}(M)} ,\end{align}where $M\in\mathbb{C}^{\texttt{CM}}_n$. We get the unique solution to theproblem, provide two Cramer's rules for the unique solution, and establish twonew expressions for the core inverse.

The core inverse and constrained matrix approximation problem