Author(s)

Phil D. Young^1*, Dean M. Young², Marsha M. Young²

¹Department of Information Systems, Baylor University, Waco, TX, USA.
²Department of Statistical Science, Baylor University, Waco, TX, USA.

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.

Matrix Equation AXB = C, Generalized Inverse Matrices, Parallel Summable Matrices, Symmetrization Device

Young, P. , Young, D. and Young, M. (2017) A General Hermitian Nonnegative-Definite Solution to the Matrix Equation AXB = C. Advances in Linear Algebra & Matrix Theory, 7, 7-17. doi: 10.4236/alamt.2017.71002.