摘要
文献对近代体上矩阵论的发展起了明显而有力的推动作用。这些文献连同文献,已经将域上矩阵的很多重要概念和结果推广到任意体,四元数体或P-除环上矩阵中。但到目前为止,系统地讨论环与体上矩阵的秩的文献却很少见。由于矩阵的秩的概念无疑是近代矩阵论中最基本、最重要的概念之一,同时也由于环中可能有零因子,以及环与体的非交换性,使得域上矩阵的某些熟知结果,如秩A=秩A′。
Let R be a non-commutative Euclid ring with a unit element 1, Ω be a skew-field with an involutorial anti-automorphism. In this paper, by using the theory and method of partitioned matrices, many important results on rank and generalized inverse in the ordinary complex matrix theory are generalized to matrices over R and Ω, we also obtain some new results and hence expand results of [1], [7]and [9].
出处
《吉林大学自然科学学报》
CSCD
1991年第1期17-20,共4页
Acta Scientiarum Naturalium Universitatis Jilinensis
关键词
环上矩阵
体上矩阵
铁
广义逆
rank of matrix (over ring), generalized inverse, generalized elimination transformation (of matrix)
