The Re-Nonnegative Definite Solutions to the Matrix Inverse Problem AX = B

Abstract

An n X n complex matrix A is termed Re-nonnegative definite (Re-nnd) if the real part of x* Ax is nonnegative for every complex n-vector x. This paper is mainly concerned with solving the following matrix inverse problem: Given complex matrices X and B, find the set of all complex Re-nnd matrices A such that AX = B.