## 分块矩阵的应用

The Application of Partitioned Matrix
Abstract: The application of partitioned matrix is an important content in the university mathematics. This paper mainly discusses some applications of block matrix. First, it introduces the definition of block matrix, properties and some simple arithmetic. Then, the paper details some special application block in the calculation and proof of the moment. Such as the use of block matrix inverse matrix problems, prove the rank of matrix product theorem and some other related applications. Finally, the application of partitioned matrix is summarized.
Keywords: The partitioned matrix; Matrix rank; Elementary transformation;    Reversible matrix

1. 预备知识    3
1.1 矩阵相关的一些定义    3
1.2 矩阵相关的一些定理    3
2．分块矩阵    4
2.1 分块矩阵的定义以及一些基本运算    4
2.2 分块乘法的初等变换    6
3． 分块矩阵的应用    6
3.1 利用分块矩阵求矩阵的乘积    6
3.2 利用分块矩阵求逆矩阵    7
3.3 利用分块矩阵求高阶行列式    9

3.4 利用分块矩阵的初等变换求矩阵的逆    13
3.5 利用分块矩阵初等变换求行列式的值    14
3.6 利用分块矩阵的初等变换求矩阵的秩    16
3.7 分块矩阵的初等变换在矩阵分解中的应用    17
4. 结束语    18

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