矩阵的秩的性质及秩的(不)等式的证明方法

The Properties of the Rank of Matrix and the Proof Methods for the Rank(In)equalities

以矩阵的秩的计算、(不)等式的证明为出发点,对常用的矩阵的秩的定义和性质进行归纳总结,并给出矩阵的秩的(不)等式的七种证明方法。通过具体例子得出结论:在证明矩阵的秩的(不)等式时,若能巧妙利用矩阵、线性方程组、线性空间、线性变换等的理论和技巧,常常能起到事半功倍的效果。

Based on the calculation of matrix rank and the proof of matrix rank(in)equalities,this paper summarizes the definition and properties of commonly used matrix rank,and gives seven proof methods of matrix rank(in)equalities.Through concrete examples,it is concluded that if we can skillfully use the theories and skills of matrix,linear equations,linear space and linear transformation,we can often get twice the result with half the effort.