On the Hermitian-Generalized Hamiltonian Solutions of Linear Matrix Equations

Abstract

By means of the properties of Hermitian-generalized Hamiltonian matrices, we give some necessary and sufficient conditions for the solvability of the matrix equation AX = B in Hermitian-generalized Hamiltonian matrix set $HHC^{n\times n}$. In the case where AX = B is solvable in $HHC^{n\times n}$, we derive the general representation of the solutions. We also give the expression of the solution for the corresponding optimal approximation problem.