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A General Hermitian Nonnegative-Definite Solution to the Matrix Equation <i>AXB</i> = <i>C</i>
Department of Information Systems, Baylor University, Waco, TX, USA
Department of Statistical Science, Baylor University, Waco, TX, USA
Department of Statistical Science, Baylor University, Waco, TX, USA
- 1 Department of Information Systems, Baylor University, Waco, TX, USA
- 2 Department of Statistical Science, Baylor University, Waco, TX, USA
- 3 Department of Statistical Science, Baylor University, Waco, TX, USA
Advances in Linear Algebra & Matrix Theory·Volume 07 (2017)·Pages 7–17·Published 15 February 2017·DOI10.4236/alamt.2017.71002
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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.
KeywordsMatrix Equation <i>AXB</i>= <i>C</i>Generalized Inverse MatricesParallel Summable MatricesSymmetrization Device
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