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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.

A General Hermitian Nonnegative-Definite Solution to the Matrix Equation &lt;i&gt;AXB&lt;/i&gt; = &lt;i&gt;C&lt;/i&gt;

A General Hermitian Nonnegative-Definite Solution to the Matrix Equation <i>AXB</i> = <i>C</i>