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Zhang, X. (2004) Hermitian Nonnegative-Definite and Positive-Definite Solutions of the Matrix Equation AXB = C. Applied Mathematics E-Notes, 4, 40-47.

has been cited by the following article:

• 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.