Abstract
In this article, we study the constrained matrix approximation problem in the Frobenius norm by using the core inverse:
||Mx-b|{|}_{F}=\hspace{.25em}\min \hspace{1em}\text{subject}\hspace{.25em}\text{to}\hspace{1em}x\in {\mathcal R} (M),
where
M\in {{\mathbb{C}}}_{n}^{\text{CM}}
. We get the unique solution to the problem, provide two Cramer’s rules for the unique solution and establish two new expressions for the core inverse.
Hartwig’s triple reverse order law for the core inverse in C∗-algebras