## 初等变换的应用

The application of elementary transformation
Abstract：Elementary transformation originated in solving linear equations, is an important idea in advanced algebra, however, we usually used primary transformation of line in a matrix in the calculation of most. In this paper is elementary row transformation in higher algebra all aspects of the application are studied, discussed the elementary transformation in the application of many advanced algebra theory, such as in the theory of linear equations, linear transformation, the vector space theory, and the theory of quadratic form aspects of the application. This topic will be elementary transformation of matrix in higher algebra systematically discusses the application of various aspects, the first write the related definitions and theorems of elementary transformation of matrix, and then discusses its related to all aspects of the application.
Keywords: elementary transformation；Matrix；System of linear equations；quadratic

1初等变换的相关概念及性质    3

1．1初等变换的相关概念    3
1．2初等变换的相关性质：    4
2初等变换的应用    4
2．1初等变换与逆矩阵    4
2.1.1逆矩阵的相关定义    4
2.1.2逆矩阵的相关性质    5
2.2.3利用初等变换求方阵的逆    5
2．2初等变换与矩阵的秩    8
2.2.1矩阵的秩的相关定义和定理    8
2.2.2用初等变换求矩阵的秩    8
2．3初等变换与线性方程组    9
2.3.1线性方程组的相关定义    9
2.3.2线性方程组的相关性质    10
2.3.3用初等变换求齐次线性方程组的解    11
2.3.4用初等变换求非齐次线性方程组的解    12
2．4初等变换与矩阵方程    14
2.4.1系数矩阵可逆的矩阵方程的解法    14
2.4.2系数矩阵不可逆的矩阵方程的解法    16
2．5初等变换与方阵的特征值    17
2.5.1矩阵的特征值的相关定义    17
2.5.2矩阵的特征值的相关性质    18
2.5.3用初等变换计算矩阵的特征值    18
2．6初等变换与矩阵对角化    19
2.6.1矩阵对角化的相关定义和定理    19
2.6.2用初等变换求解矩阵的相似对角化    20
2．7用初等变换化二次型为标准形    22
2．8矩阵的初等变换在向量空间中的应用    24
2.8.1用初等变换求列向量组的线性关系    24
2.8.2线性表示的求法    24
2.8.3初等变换在求向量组的极大无关组中的应用    26
2.8.4等价向量组的判定    26 源`自<六:维;论-文>网/www.lwfree.cn
2．9初等变换在多项式理论中的应用    27
2.9.1用矩阵的初等变换求最大公因式    28 初等变换的应用:http://www.lwfree.cn/shuxue/20190929/40139.html
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