TITLE:
A General Hermitian Nonnegative-Definite Solution to the Matrix Equation AXB = C
AUTHORS:
Phil D. Young, Dean M. Young, Marsha M. Young
KEYWORDS:
Matrix Equation AXB = C, Generalized Inverse Matrices, Parallel Summable Matrices, Symmetrization Device
JOURNAL NAME:
Advances in Linear Algebra & Matrix Theory,
Vol.7 No.1,
March
7,
2017
ABSTRACT: We derive necessary and sufficient conditions for the existence of a Hermitian nonnegative-definite solution to the matrix equation AXB = C. Moreover, we derive a representation of a general Hermitian nonnegative-definite solution. We then apply our solution to two examples, including a comparison of our solution to a proposed solution by Zhang in [1] using an example problem given from [1]. Our solution demonstrates that the proposed general solution from Zhang in [1] is incorrect. We also give a second example in which we derive the general covariance structure so that two matrix quadratic forms are independent.