## 关于方阵对角化问题的初步探究

The Preliminary Inquiry Ａbout Square Matrix Diagonalization Problem
Abstract：As a special matrix, the theories of square matrix could be applied throughout determinant, linear equations, linear space, linear transformation, and quadratic forms etc. The square matrix diagonalization as the most simple square matrix , is significant in both theories and applications. The inquiry of square matrix diagonalization problem is a basic problem in phalanx theory. The aim of this study is to have a comprehensive understanding of square matrix diagonalization and the sufficient and necessary condition of diagonolization phalanx.In addition, it’s of great importance for us to understand the basic content of square matrix diagonalization, as well as grasp the methods. Mastering the methods of square matrix diagonalization should be taken in the first position. Moreover, after studying the problem of square matrix diagonalization in this paper, we are ought to innovate in some ways ang have a promotion in pergent thinking.
Key words：Square matrix; Square matrix diagonalization; Sufficient and necessary condition; application.

1.方阵的相关概念及定理    3
1.1方阵的相关概念及其性质    3
1.2方阵的相关定理    4
1.3方阵的特征值与特征向量    4
1.4  方阵的相关概念    5
2.方阵可对角化的条件及方法    5
2.1方阵可对角化的概念    5
2.2特征值和特征与方阵对角化    6
2.3相似变换与方阵对角化    8
2.4  -方阵与方阵对角化    13
3.几种特殊方阵可对角化    14
3.1实对称矩阵的对角化    14
3.2循回方阵的对角化    14
3.3对合矩阵一定可以对角化    15
3.4幂等矩阵一定可以对角化    16

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