线性映射方法在矩阵秩的性质证明中的应用

Application of Linear Mapping Method in Proving Properties of Matrix Rank

计算或证明矩阵秩的性质因为需要许多技巧而一直都是一个难题,即使有些性质用矩阵的方法可证,但也相当复杂麻烦.本文将线性空间、线性映射的概念与矩阵的秩联系起来,证明了几个矩阵秩的性质,此方法可将已有的复杂证明过程简单化.

The property calculation or proof of matrix rank is always a difficult problem because of requi- ting many techniques. Even if some properties can be proved by matrix method, it is also complicated. By link- ing the concept of linear space and linear mapping with the rank of matrix, several properties of matrix rank were proved in the paper, and the method can simplify the existed complex proof processes.