Abstract :
Recently, Wu and Cain [L. Wu, B. Cain, Linear Algebra and its Applications 236 (1996) 137–146] gave necessary and sufficient conditions for the matrix equationAX = B to have a solution with respect toA subject to the condition that the Hermitian part ofA is non-negative definite. In this note we give an easier approach, which also provides possible explicit expressions forA. Further, necessary and sufficient conditions are derived when the Hermitian part ofA is prescribed to be positive definite, thus correcting a result in [L. Wu, B. Cain, Linear Algebra and its Applications 236 (1996) 137–146, Theorem 5].
