In this paper, a lower bound of maximal dimensions of commutable matrix spaces (CMS) is given. It is found that the linear dependence of a group of one to one commutable matrices is related to whether some equations i...In this paper, a lower bound of maximal dimensions of commutable matrix spaces (CMS) is given. It is found that the linear dependence of a group of one to one commutable matrices is related to whether some equations in system can be eliminated. The corresponding relation is given. By introducing conceptions of eliminating set and eliminating index, we give an estimation of upper bound of maximal dimensions of CMS. For special cases n=5,6, the further estimation of maximal dimensions of CMS is presented.展开更多
We give an affirmative answer to the open problem proposed by Dr， Fuzhen Zhang in the paper 'Quaternions and matrices of quaternious'( LA A251:21-57 ) ,that is, there exists a 2n × 2n complex matrix B ...We give an affirmative answer to the open problem proposed by Dr， Fuzhen Zhang in the paper 'Quaternions and matrices of quaternious'( LA A251:21-57 ) ,that is, there exists a 2n × 2n complex matrix B such that, for any n×n complex matrices A1, A2展开更多
基金Supported by the Youth Mainstay Teacher Foundation of HunanProvince Educational Committee
文摘In this paper, a lower bound of maximal dimensions of commutable matrix spaces (CMS) is given. It is found that the linear dependence of a group of one to one commutable matrices is related to whether some equations in system can be eliminated. The corresponding relation is given. By introducing conceptions of eliminating set and eliminating index, we give an estimation of upper bound of maximal dimensions of CMS. For special cases n=5,6, the further estimation of maximal dimensions of CMS is presented.
文摘We give an affirmative answer to the open problem proposed by Dr， Fuzhen Zhang in the paper 'Quaternions and matrices of quaternious'( LA A251:21-57 ) ,that is, there exists a 2n × 2n complex matrix B such that, for any n×n complex matrices A1, A2
