- 电子工业出版社
- 9787121508677
- 1-3
- 568590
- 平塑
- 16开
- 2025-12
- 242
- 148
- 理学
- 数学类
- 数学
- 本科
内容简介
本书依据教育部高等学校大学数学课程教学指导委员会制定的《大学数学课程教学基本要求（2014 年版）》，适应地方经济发展对应用型人才培养的要求，围绕教学大纲编写而成．在编写的过程中，吸收了国内现有教材的优点，适当地加入了一些线性代数的应用，在方便教师教学和学生自学方面做了尝试．本书知识体系完整，内容编排结构合理，语言简洁明了． 本书内容包括行列式、矩阵、向量组和向量空间、线性方程组、矩阵的对角化及二次型、线性代数的一些应用．本书还嵌入一些题目的讲解视频二维码和习题答案二维码，读者可扫码查看．
目录
第1 章 行列式······························································································· 1
1.1 n 阶行列式························································································· 1
1.1.1 二阶行列式和三阶行列式······························································ 1
1.1.2 n 阶行列式的定义······································································· 4
1.2 行列式的性质····················································································· 7
1.2.1 行列式的性质············································································· 7
1.2.2 利用行列式的性质进行计算·························································· 10
1.3 行列式按行（列）展开········································································ 12
1.3.1 余子式与代数余子式··································································· 12
1.3.2 行列式按行（列）展开定理·························································· 13
1.3.3 范德蒙行列式············································································ 16
1.4 克莱姆法则······················································································· 18
1.4.1 齐次线性方程组与非齐次线性方程组·············································· 18
1.4.2 克莱姆法则··············································································· 18
习题1····································································································· 21
第2 章 矩阵································································································· 25
2.1 矩阵································································································ 25
2.1.1 矩阵的概念··············································································· 25
2.1.2 几种特殊的矩阵········································································· 27
2.1.3 矩阵的相等··············································································· 28
2.2 矩阵的运算······················································································· 28
2.2.1 矩阵的基本运算········································································· 28
2.2.2 矩阵的转置··············································································· 32
2.2.3 方阵的幂·················································································· 33
2.2.4 方阵的行列式············································································ 35
2.2.5 伴随矩阵·················································································· 35
2.3 逆矩阵····························································································· 36
2.3.1 逆矩阵的概念及其求法································································ 36
2.3.2 逆矩阵的性质············································································ 39
2.4 分块矩阵·························································································· 41
2.4.1 分块矩阵的定义········································································· 41
2.4.2 分块矩阵的运算········································································· 42
2.4.3 特殊的分块矩阵········································································· 44
2.5 矩阵的初等变换和初等矩阵·································································· 46
2.5.1 矩阵的初等变换········································································· 46
2.5.2 初等矩阵·················································································· 48
2.5.3 初等变换的应用········································································· 52
2.6 矩阵的秩·························································································· 53
2.6.1 矩阵的秩的概念········································································· 53
2.6.2 矩阵的秩的计算········································································· 54
2.6.3 矩阵的秩的性质···················
1.1 n 阶行列式························································································· 1
1.1.1 二阶行列式和三阶行列式······························································ 1
1.1.2 n 阶行列式的定义······································································· 4
1.2 行列式的性质····················································································· 7
1.2.1 行列式的性质············································································· 7
1.2.2 利用行列式的性质进行计算·························································· 10
1.3 行列式按行（列）展开········································································ 12
1.3.1 余子式与代数余子式··································································· 12
1.3.2 行列式按行（列）展开定理·························································· 13
1.3.3 范德蒙行列式············································································ 16
1.4 克莱姆法则······················································································· 18
1.4.1 齐次线性方程组与非齐次线性方程组·············································· 18
1.4.2 克莱姆法则··············································································· 18
习题1····································································································· 21
第2 章 矩阵································································································· 25
2.1 矩阵································································································ 25
2.1.1 矩阵的概念··············································································· 25
2.1.2 几种特殊的矩阵········································································· 27
2.1.3 矩阵的相等··············································································· 28
2.2 矩阵的运算······················································································· 28
2.2.1 矩阵的基本运算········································································· 28
2.2.2 矩阵的转置··············································································· 32
2.2.3 方阵的幂·················································································· 33
2.2.4 方阵的行列式············································································ 35
2.2.5 伴随矩阵·················································································· 35
2.3 逆矩阵····························································································· 36
2.3.1 逆矩阵的概念及其求法································································ 36
2.3.2 逆矩阵的性质············································································ 39
2.4 分块矩阵·························································································· 41
2.4.1 分块矩阵的定义········································································· 41
2.4.2 分块矩阵的运算········································································· 42
2.4.3 特殊的分块矩阵········································································· 44
2.5 矩阵的初等变换和初等矩阵·································································· 46
2.5.1 矩阵的初等变换········································································· 46
2.5.2 初等矩阵·················································································· 48
2.5.3 初等变换的应用········································································· 52
2.6 矩阵的秩·························································································· 53
2.6.1 矩阵的秩的概念········································································· 53
2.6.2 矩阵的秩的计算········································································· 54
2.6.3 矩阵的秩的性质···················
