关于矩阵的秩的等价描述

Description of the Equivalent Propositions on the Rank of Matrix

从行列式、矩阵的等价、线性方程组、线性空间、线性映射等角度来刻画矩阵的秩,进而用这些命题来证明与矩阵的秩有关的一些命题.

In this note, we describe the equivalent propositions on the rank of matrix by determinants, equivalent of matrix, system of linear equations, linear space, linear mapping and so on. On the contrary, we prove a property of the rank of matrix by the equivalent theorems.