The complete equivalence canonical form of four matrices over an arbitrary division ring |
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| Authors: | Zhuo-Heng He Yang Zhang |
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| Institution: | 1. Department of Mathematics, Shanghai University, Shanghai, P.R. China.;2. Department of Mathematics and Statistics, Auburn University, Auburn, USA.;3. Department of Mathematics, University of Manitoba, Winnipeg, Canada. |
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| Abstract: | In this paper, we give the complete structures of the equivalence canonical form of four matrices over an arbitrary division ring. As applications, we derive some practical necessary and sufficient conditions for the solvability to some systems of generalized Sylvester matrix equations using the ranks of their coefficient matrices. The results of this paper are new and available over the real number field, the complex number field, and the quaternion algebra. |
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| Keywords: | Matrix decomposition division ring generalized Sylvester matrix equations rank Hermite matrix |
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