矩阵的秩是指矩阵中行（或列）向量组的秩，与之等价的说法通常是指矩阵中不为零的子式的最高阶数，是矩阵最重要的数字特征之一。

基于矩阵的秩在高等代数学中的重要性，本文系统总结了矩阵的秩的基本性质,以及对矩阵的秩在满秩分解,公式和一类恒等式等方面的应用。

关键词：矩阵；秩；分块矩阵；初等变换
ABSTRACT
The matrix rank is refers to the matrix the line (or row) the vector groups order, usually is refers to the matrix with it equal view is not zero minor highest exponent number, is one of matrix most important digit characteristics .Based on the matrix rank in higher algebras importance, this article summed up matrix rank some nature, as well as decomposes to the matrix rank in the non-singular, aspect and so on a formula and kind of identical equation applications.
Key word: matrix; rank; partitioned matrix; elemetary operation。