The Re-nonnegative definite solutions to the matrix inverse problem AX = B Original Research Article

An n × n complex matrix A is termed Re-nonnegative definite (Re-nnd) if the real part of x*Ax is nonnegative for every complex n-vectorx. 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.