English

The complete equivalence canonical form of four matrices over an arbitrary division ring

Rings and Algebras 2017-02-03 v2

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.

Keywords

Cite

@article{arxiv.1608.06046,
  title  = {The complete equivalence canonical form of four matrices over an arbitrary division ring},
  author = {Zhuo-Heng He and Qing-Wen Wang and Yang Zhang},
  journal= {arXiv preprint arXiv:1608.06046},
  year   = {2017}
}