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Zbl 1149.15012
Wang, Qing-Wen; Yu, Shao-Wen; Lin, Chun-Yan
Extreme ranks of a linear quaternion matrix expression subject to triple quaternion matrix equations with applications. (English)
[J] Appl. Math. Comput. 195, No. 2, 733-744 (2008). ISSN 0096-3003

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.
[Mihail M. Konstantinov (Sofia)]

MSC 2000:: *15A24 Matrix equations
15A33 Matrices over special rings
15A09 Matrix inversion

Keywords: quaternion matrix equations, extreme rank, generalized inverse; Schur complement

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