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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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