矩阵秩的不同定义及其比较

Different Definitions of Matrix Rank and Comparation

秩是矩阵固有的特性,是矩阵分析的基础.从矩阵的初等变换出发.给出秩的第三定义,证明了秩的三种定义的等价性,并比较了三种定义的优劣.

Rank is an inherent characteristic of matrix and it is the basis of matrix analysis.In this paper,we give a third definition on the rank of matrix from the well-known elementary transformation of matrices,and show the equivalence of the three definitions.Finally,we compare the advantages and disadvantages of the three definitions.