关于除环上分块矩阵秩的等式

On Rank Equalities of Partitioned Matrices over a Division Ring

中文关键词:  除环  分块矩阵  秩等式  双矩阵分解

英文关键词:Division ring  partitioned matrix  rank equalities  decomposition of pairwise matrices.

中文摘要:

      本文使用双矩阵分解方法研究除环上分块矩阵秩的等式,给出了Marsaglia-Styan公式一个新的证明并获得了一些新的秩等式的刻划.

英文摘要:

      By applying the decomposition of the pairwise matrices over a division ring, we give a new proof of Marsaglia-Styan rank formula. We also obtain some equivalent characterizations of some new rank equalities of the partitioned matrices.