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On Positive Definite Solutions of Quaternionic Matrix Equations

The real representation of the quaternionic matrix is definited and studied. The relations between the positive (semi)define quaternionic matrix and its real representation matrix are presented. By means of the real representation, the relation between the positive (semi)definite solutions of quaternionic matrix equations and those of corresponding real matrix equations is established. Keywords—Matrix equation, Quaternionic matrix, Real representation, positive (semi)definite solutions.