摘要:矩阵在高等数学中是很多分支研究问题的一个重要性的工具,同时也是高等代数中重点讲述的概念。通常在理论研究中和实际应用中,我们可能会遇到结构比较特殊或者是级数较高的大矩阵,为了方便分析处理相关问题,我们会按照矩阵的性状或者是实践的需要来对所谈论的矩阵进行适当的划分，将一些大的矩阵按照一定规则分成一些阶数较低的子矩阵,这就是矩阵的分块。分块矩阵是解决相关矩阵问题的关键性所在,应用也非常广泛。利用分块矩阵的方法能够降低矩阵的阶数,使矩阵的结构层次变得清晰明了,从而使矩阵的运算变得简单,并使有关矩阵的计算和证明方面的问题得以迅速的解决,所以分块矩阵在处理一些矩阵问题方面有着不可或缺的作用。正文从分块矩阵的基本概念,加法及数乘等运算,分块方法,求逆矩阵和行列式,矩阵的秩以及在线性方程组中的应用方面进行了相关研究及探讨,并举出与计算和证明有关的例题来表明利用分块矩阵可以令高等代数中的很多问题得以方便解决。 83869

毕业论文关键词：分块矩阵；逆矩阵；行列式；矩阵的秩；线性方程组

On the Operation and Application of Block Matrix

Abstract : Matrix is ​​a question of the importance of many branches of research tools in higher mathematics, but also the concept of Higher Algebra focuses Typically in theoretical study and practical application, we may have a more specific structure or progression compared high large matrix, in order to facilitate analysis and processing related issues, we will follow the characters or the need to practice a matrix appropriate pision of the matrix are talking about, some of the large matrix according to certain rules into some of the lower order sub matrix, which is the block matrix。 partitioned matrix is ​​a key to solve the problem where the correlation matrix, is also widely used。 use block matrix method can reduce the order of the matrix so that the matrix becomes clear hierarchy, so that the matrix operations easier, and computing and related issues proofs of the matrix are quickly resolved, so that the block matrix has an indispensable role in addressing some of the issues matrix。 the basic concepts of the text from the block matrix , addition and multiplication and other operations, block method, matrix inversion and determinant, rank, and applications of linear matrix equations were related research and discussion, citing the example of calculations and prove to show that the use partitioned matrix can make many of the advanced algebra problem is easy to solve。

Keywords : Block Matrix; Inverse Matrix; Determinant; Rank of Matrix; Linear Equations 

目录

摘要 3

引言 3

1。分块矩阵的基本概念 3

2。分块矩阵的初等变换 3

3。分块矩阵的运算 3

3。1分块矩阵的加法与数量乘法 3

3。2分块矩阵的乘法运算 3

3。3分块矩阵的转置 3

4。分块矩阵的应用 3

4。1利用分块矩阵求矩阵的逆 3

4。2分块矩阵在行列式中的应用 3

4。2。1利用分块矩阵求矩阵的行列式 3

4。2。2利用分块矩阵证明有关矩阵行列式的等式 3

4。3在线性方程组中的应用 3

4。4证明矩阵秩的不等式