The Solutions to Matrix Equation AX=B with Some Constraints

Abstract

Let $P$ be a given Hermitian matrix satisfying $P^2=I$. Using the eigenvalue decomposition of $P$, we consider the least squares solutions to the matrix equation $AX=B$ with the constraints $PX=XP$ and $X^{\mathrm{*}}=X$. A similar problem of this matrix equation with generalized constrained is also discussed.