Hermitian and non-negative definite reflexive and anti-reflexive solutions to AX=B
Xifu Liu · International Journal of Computer Mathematics · 2017
In this paper, we establish some conditions for the existence and the representations for the Hermitian reflexive and Hermitian anti-reflexive, and non-negative definite reflexive solutions to the matrix equation AX=B with respect to a generalized reflection matrix P by using the Moore–Penrose inverse. Moreover, in corresponding solution sets of the equation, the explicit expressions of the nearest matrix to a given matrix in the Frobenius norm have been provided.