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# 矩阵的等价关系及其应用（毕业设计论文doc）.doc

Equivalence Relations between Matrix
And It’s Applications

【摘要】等价关系是指满足自反性、对称性和传递性这三种性质的关系。矩阵的等价关系有三种:矩阵的等价、矩阵的相似、矩阵的合同。由矩阵间的三种等价关系及每种关系各自存在的条件,我们可以得出矩阵的这三种等价关系间的联系。利用矩阵的等价关系及它们之间的联系,可以解决矩阵的许多问题。本文从矩阵的概念入手,论述了矩阵的等价、矩阵的相似、矩阵的合同这三种等价关系的概念及其性质,以及它们之间的联系和区别。在此基础上,还给出了对矩阵的这三种等价关系的一些应用,其中主要是矩阵对角化的应用。
【关键词】矩阵的等价,矩阵的相似,矩阵的合同,对角化
Equivalence Relations between Matrix
And it’s Applications
Juan Huang
【Abstract】Equivalence relation is the relationship that satisfy the condition of reflexivity, symmetry and transitive. There are three kinds of equivalence relations between matrix: Equivalent, similarity, congruence of matrix. Through analyzing three equivalence relations between matrix and conditions satisfied by each existed relation, we can find the connection between these relations. Use the equivalence relations between matrix and the connection between them, we can solve many problems about matrix. This article starts from the definition of matrix, and then we illustrate the idea and nature of the three equivalents of matrix, and the connection and difference between them. Base on this, this paper puts some applications of the three equivalent relations of matrix, and the main key is the application of matrix diagonalization.
【Key words】Equivalent of matrix,Similarity of matrix,Congruence of matrix, Diagonalization

1 引言 1
2 矩阵的基本概念 1

3 矩阵的等价关系 2

4 矩阵等价、相似、合同的联系 6
5 矩阵等价关系的一些应用 7

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1 引言

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