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Extreme ranks of a linear quaternion matrix expression subject to triple quaternion matrix equations with applications. (English) Zbl 1149.15012
Maximal and minimal ranks of the quaternion matrix \(C_4 - A_4XB_4\) are studied, where \(X\) is a variable quaternion matrix subject to the quaternion equations \(A_1X = C_1\), \(XB_2 = C_2\), \(A_3XB_3 = C_3\). As a corollary necessary and sufficient conditions for solvability of a system of quaternion matrix equations are obtained. Extremal ranks of the generalized Schur complement of a certain matrix (under some linear constraints) are also studied. The paper generalizes some previous results in this area.

MSC:
15A24 Matrix equations and identities
15B33 Matrices over special rings (quaternions, finite fields, etc.)
15A09 Theory of matrix inversion and generalized inverses
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