除环上矩阵的子矩阵的秩的恒等式与不等式

本文提供了除环上矩阵的一些子矩阵的秩的若干恒等式与不等式,出现在本文中的这些结果,在处理涉及某些应用方面的复矩阵(作为除环上矩阵的特例)问题以及某些纯数学问题将起重要作用。

Identities and Inequalities on the Rank for some Submatrices of a Matrix over a Division Ring

This paper studies the "substructure" of a matrix over the division ring, and provides an inequality on the rank for the submatrix of the product of two matrices, and an identity on the rank for the submatrix of an inverting matrix. An inequality On the rank of the submatrix of a nonsingular matrix is also given. Some applications of the above conclusions is provided also, one of the interesting results is that the rank of every (n- 1 ) × (n- 1) submatrix of an n × n nonsingular matrix is at least n-2.