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Zbl 1124.15010
Wang, Qing-Wen; Song, Guang-Jing; Lin, Chun-Yan
Extreme ranks of the solution to a consistent system of linear quaternion matrix equations with an application.
(English)
[J] Appl. Math. Comput. 189, No. 2, 1517-1532 (2007). ISSN 0096-3003

The authors establish the maximal and minimal ranks of the solution to the consistent system of quaternion matrix equations $A_1X=C_1, A_2X=C_2$, $A_3XB_3=C_3$ and $A_4XB_4=C_4$, recently investigated by {\it Q. W. Wang} [Comput. Math. Appl. 49, 665--675 (2005; Zbl 1138.15004)]. As an application, a necessary and sufficient condition for the invariance of the rank of the general solution to the system mentioned above is presented.
[A. Arvanitoyeorgos (Rion)]
MSC 2000:
*15A24 Matrix equations
15A03 Vector spaces
15A33 Matrices over special rings

Keywords: system of quaternion matrix equations; minimal rank; generalized inverse; maximal rank

Citations: Zbl 1138.15004

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