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Extreme ranks of the solution to a consistent system of linear quaternion matrix equations with an application. (English) Zbl 1124.15010
The authors establish the maximal and minimal ranks of the solution to the consistent system of quaternion matrix equations A 1 X=C 1 ,A 2 X=C 2 , A 3 XB 3 =C 3 and A 4 XB 4 =C 4 , recently investigated by 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.
15A24Matrix equations and identities
15A03Vector spaces, linear dependence, rank
15A33Matrices over special rings