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2018年硕士研究生入学考试自命题科目考试大纲-819-高等代数

2018年硕士研究生入学考试自命题科目考试大纲-819-高等代数

2018年全国硕士研究生入学统一考试

数学专业《高等代数》考试大纲

一、考核目标

《高等代数》考试考察考生是否具备攻读数学专业的硕士研究生所必须的代数基础和基本素养,高等代数是数学专业的一门重要的基础课程,主要包括行列式、线性方程组、矩阵、二次型、多项式理论、线性空间与线性变换等。要求考生能准确理解高等代数中的基本思想、基本概念,熟练掌握高等代数中的各种基本计算和论证技巧,具备综合运用代数理论解决具体问题的能力。

二、考试主要范围

1.数域与排列;

2.行列式的性质与计算;

3.克莱姆法则;

4.向量组的线性相关性、极大无关组;

5.向量组的秩、矩阵的秩;

6.线性方程组及其解的结构;

7.矩阵的运算与初等变换,初等矩阵;

8.二次型及其标准型;

9.正定二次型;

10.多项式理论;

11.线性空间的基与坐标;

12.线性子空间的交与和;

13.线性变换;

14.特征值与特征向量;

15.矩阵相似与对角化、若当标准形;

16.标准正交基与正交变换

17.实对称矩阵的正交相似对角化。

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一、

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