线性代数慕课版张天德玮学生基础知识技能MATLAB应用大中专教辅研究生专科本科人民邮电出版社山东大学数学学院

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线性代数慕课版张天德玮学生基础知识技能MATLAB应用大中专教辅研究生专科本科人民邮电出版社山东大学数学学院
线性代数慕课版张天德玮学生基础知识技能MATLAB应用大中专教辅研究生专科本科人民邮电出版社山东大学数学学院
线性代数慕课版张天德玮学生基础知识技能MATLAB应用大中专教辅研究生专科本科人民邮电出版社山东大学数学学院
线性代数慕课版张天德玮学生基础知识技能MATLAB应用大中专教辅研究生专科本科人民邮电出版社山东大学数学学院

线性代数慕课版张天德玮学生基础知识技能MATLAB应用大中专教辅研究生专科本科人民邮电出版社山东大学数学学院

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线性代数慕课版张天德玮学生基础知识技能MATLAB应用大中专教辅研究生专科本科人民邮电出版社山东大学数学学院

线性代数慕课版张天德玮学生基础知识技能MATLAB应用大中专教辅研究生专科本科人民邮电出版社山...

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商品详情
线性代数(慕课版)
定价
45.00
出版社
人民邮电出版社
版次
1
出版时间
2021年02月
开本
16
作者
张天德,王玮
页数
字数
ISBN编码
9787115536662
重量
本书将新工科理念与国际化深度融合,借鉴国内外优秀教材的特点,并结合山东大学数学团队多年的教学经验编写完成。本书共6章,内容包括行列式、矩阵、向量与向量空间、线性方程组、矩阵的特征值与特征向量、二次型。每节配有难易适中的同步习题,各章配有总复习题,同时辅以思维导图、MATLAB应用等新形势和新内容,帮助学生巩固和掌握基础知识和基本技能。
01
第1 章 行列式.............. 1
1.1 行列式的基本概念................... 1
1.1.1 排列及其逆序数.................... 1
1.1.2 二阶、三阶行列式................ 2
1.1.3 n 阶行列式........................... 5
同步习题1.1................................... 8
1.2 行列式的性质及其应用.............9
1.2.1 行列式的性质....................... 9
1.2.2 行列式性质的简单应用....... 12
同步习题1.2................................. 14
1.3 行列式的典型计算方法........... 15
1.3.1 上(下)三角法 ................. 15
1.3.2 降阶法.............................. 17
*1.3.3 升阶法............................. 18
1.3.4 拆分法.............................. 20
*1.3.5 递推法............................. 21
同步习题1.3................................. 24
1.4 克莱姆法则......................... 25
同步习题1.4................................. 28
1.5 运用MATLAB 计算行列式.... 29
1.5.1 MATLAB 简介................... 29
1.5.2 用MATLAB 计算行列式.... 30
第1 章思维导图.......................... 31
第1 章总复习题.......................... 32
第2 章 矩阵..............35
2.1 矩阵的基本概念................... 35
2.1.1 引例.................................. 35
2.1.2 矩阵的定义........................ 36
2.1.3 几种特殊矩阵.................... 37
同步习题2.1.................................40
2.2 矩阵的运算......................... 40
2.2.1 矩阵的线性运算.................40
2.2.2 线性变换与矩阵乘法.......... 41
2.2.3 矩阵的转置....................... 47
2.2.4 方阵的行列式.................... 48
2.2.5 伴随矩阵...........................49
同步习题2.2................................ 50
2.3 初等变换与初等矩阵............. 51
2.3.1 矩阵的初等变换................. 51
2.3.2 初等矩阵........................... 52
同步习题2.3................................ 55
2.4 逆矩阵.............................. 56
2.4.1 逆矩阵的定义.................... 56
2.4.2 矩阵可逆的充要条件.......... 57
2.4.3 矩阵之间的等价关系.......... 59
2.4.4 解矩阵方程....................... 62
同步习题2.4................................ 64
2.5 矩阵的秩........................... 65
目 录
02
2 线性代数(慕课版)
2.5.1 矩阵秩的定义..................... 65
2.5.2 矩阵秩的性质.................... 66
2.5.3 矩阵秩的相关结论............. 68
同步习题2.5................................ 69
2.6 分块矩阵........................... 70
2.6.1 分块矩阵的定义................. 70
2.6.2 分块矩阵的运算................. 71
2.6.3 分块对角矩阵.................... 73
同步习题2.6................................ 76
2.7 运用MATLAB 进行矩阵
运算................................. 77
2.7.1 矩阵的加法........................ 77
2.7.2 矩阵的乘法、数乘、乘方... 78
2.7.3 求矩阵的转置.................... 78
2.7.4 求矩阵的逆....................... 78
2.7.5 求矩阵的行#简形.............. 79
第2 章思维导图..........................80
第2 章总复习题.......................... 81
03
第3 章 向量与向量
空间..............84
3.1 n 维向量及其线性运算........... 84
3.1.1 n 维向量的定义.................. 84
3.1.2 n 维向量的线性运算........... 85
同步习题3.1................................. 86
3.2 向量组的线性关系................ 86
3.2.1 向量组的线性组合.............. 86
3.2.2 向量组的等价.................... 87
3.2.3 线性组合的经济学应用
举例................................. 88
3.2.4 向量组线性相关性的
定义................................. 88
3.2.5 向量组线性相关性的
性质.................................90
3.2.6 向量组线性相关性的
判定................................. 92
同步习题3.2................................ 93
3.3 极大线性无关组和秩............. 95
3.3.1 极大线性无关组和向量组
的秩................................. 95
3.3.2 向量组的秩和矩阵的秩的
关系................................. 96
同步习题3.3................................98
3.4 向量空间........................... 99
3.4.1 向量空间的定义.................99
*3.4.2 过渡矩阵与坐标变换....... 100
同步习题3.4.............................. 102
3.5 向量的内积....................... 102
3.5.1 向量的内积的定义............ 102
3.5.2 向量组的正交规范化........ 104
3.5.3 正交矩阵......................... 105
同步习题3.5.............................. 106
3.6 运用MATLAB 解决向量
问题............................... 106
3.6.1 判断向量组的线性
相关性............................ 107
3.6.2 求极大无关组.................. 107
目录3
3.6.3 将向量组正交规范化........ 107
第3 章思维导图........................ 109
第3 章总复习题.........................110
04
第4 章 线性方程组....112
4.1 齐次线性方程组..................112
4.1.1 引例.................................112
4.1.2 齐次线性方程组解的性质....113
4.1.3 齐次线性方程组的
基础解系..........................113
同步习题4.1................................117
4.2 非齐次线性方程组...............119
4.2.1 非齐次线性方程组的基本
概念................................119
4.2.2 非齐次线性方程组解的
性质............................... 120
4.2.3 非齐次线性方程组的
解法............................... 120
同步习题4.2.............................. 125
4.3 线性方程组的应用.............. 127
4.3.1 向量组与线性方程组........ 127
4.3.2 利用线性方程组解的理论
求解线性方程组............... 129
4.3.3 矩阵方程与线性方程组..... 130
4.3.4 同解与公共解.................. 132
4.3.5 线性方程组应用案例........ 135
同步习题4.3.............................. 137
4.4 运用MATLAB 求解线性
方程组............................ 139
4.4.1 求解齐次线性方程组........ 139
4.4.2 求解非齐次线性方程组..... 139
第4 章思维导图.........................141
第4 章总复习题........................ 142
05
第5 章 矩阵的特征值与
特征向量...... 145
5.1 特征值与特征向量.............. 145
5.1.1 特征值与特征向量的
定义............................... 145
5.1.2 特征值与特征向量的
性质............................... 148
同步习题5.1................................151
5.2 相似矩阵......................... 152
5.2.1 相似矩阵的定义及性质..... 152
5.2.2 方阵的相似对角化........... 153
同步习题5.2.............................. 157
5.3 实对称矩阵及其对角化 ........ 159
5.3.1 实对称矩阵的特征值与特征
向量............................... 159
5.3.2 实对称矩阵的正交相似
对角化............................ 159
同步习题5.3.............................. 164
5.4 运用MATLAB 求解矩阵
问题............................... 165
4 线性代数(慕课版)
5.4.1 求特征值与特征向量......... 165
5.4.2 矩阵对角化的判断........... 166
第5 章思维导图........................ 168
第5 章总复习题........................ 169
06
第6 章 二次型..........171
6.1 二次型及其矩阵表示.............171
6.1.1 二次型的定义....................171
6.1.2 二次型及其矩阵............... 172
同步习题6.1............................... 173
6.2 二次型的标准形................. 174
6.2.1 利用正交变换法化二次型
为标准形......................... 174
6.2.2 利用配方法化二次型为
标准形............................ 177
同步习题6.2.............................. 178
6.3 正定二次型....................... 179
6.3.1 正定二次型的定义............ 179
6.3.2 赫尔维茨定理.................. 180
同步习题6.3...............................181
6.4 用MATLAB 进行二次型的
运算............................... 182
6.4.1 化二次型为标准形............ 182
6.4.2 正定二次型的判定........... 183
第6 章思维导图........................ 183
第6 章总复习题........................ 184
附录 线性代数中的数学
建模................ 186
参考答案 .................. 190
即时提问答案........................... 190
同步习题答案........................... 193
总复习题答案........................... 206
山东大学数学学院教授,泰山学堂主讲教师,山东数学会高等数学专业委员会主任,全国大学生数学竞赛山东赛区负责人,全国微课程比赛山东赛区副主任兼秘书长,中国大学先修课程《微积分》特聘教授。作为主要成员完成国家科学基金及山东省自然科学基金项目6项,主持或参与省部级教学研究项目5项;发表学术论文50余篇;参与编写的《微积分》入选国家十二五规划教材;曾获“山东省中青年学术骨干、学科带头人”等称号。

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重要公告
本店不会以境外电话联系顾客有关书籍相关信息,如有接到境外电话或者拉您进qq群谈及理赔相关事宜请广大顾客不要相信,不要按照电话内容操作,谨防诈骗!快递丢件(可以联系当地派件员)
任何问题以联系店铺在线客服为准。

标题、详情出版时间等有误差

 

具体出版信息以咨询在线客服为准

商品详情
线性代数(慕课版)
定价
45.00
出版社
人民邮电出版社
版次
1
出版时间
2021年02月
开本
16
作者
张天德,王玮
页数
字数
ISBN编码
9787115536662
重量
本书将新工科理念与国际化深度融合,借鉴国内外优秀教材的特点,并结合山东大学数学团队多年的教学经验编写完成。本书共6章,内容包括行列式、矩阵、向量与向量空间、线性方程组、矩阵的特征值与特征向量、二次型。每节配有难易适中的同步习题,各章配有总复习题,同时辅以思维导图、MATLAB应用等新形势和新内容,帮助学生巩固和掌握基础知识和基本技能。
01
第1 章 行列式.............. 1
1.1 行列式的基本概念................... 1
1.1.1 排列及其逆序数.................... 1
1.1.2 二阶、三阶行列式................ 2
1.1.3 n 阶行列式........................... 5
同步习题1.1................................... 8
1.2 行列式的性质及其应用.............9
1.2.1 行列式的性质....................... 9
1.2.2 行列式性质的简单应用....... 12
同步习题1.2................................. 14
1.3 行列式的典型计算方法........... 15
1.3.1 上(下)三角法 ................. 15
1.3.2 降阶法.............................. 17
*1.3.3 升阶法............................. 18
1.3.4 拆分法.............................. 20
*1.3.5 递推法............................. 21
同步习题1.3................................. 24
1.4 克莱姆法则......................... 25
同步习题1.4................................. 28
1.5 运用MATLAB 计算行列式.... 29
1.5.1 MATLAB 简介................... 29
1.5.2 用MATLAB 计算行列式.... 30
第1 章思维导图.......................... 31
第1 章总复习题.......................... 32
第2 章 矩阵..............35
2.1 矩阵的基本概念................... 35
2.1.1 引例.................................. 35
2.1.2 矩阵的定义........................ 36
2.1.3 几种特殊矩阵.................... 37
同步习题2.1.................................40
2.2 矩阵的运算......................... 40
2.2.1 矩阵的线性运算.................40
2.2.2 线性变换与矩阵乘法.......... 41
2.2.3 矩阵的转置....................... 47
2.2.4 方阵的行列式.................... 48
2.2.5 伴随矩阵...........................49
同步习题2.2................................ 50
2.3 初等变换与初等矩阵............. 51
2.3.1 矩阵的初等变换................. 51
2.3.2 初等矩阵........................... 52
同步习题2.3................................ 55
2.4 逆矩阵.............................. 56
2.4.1 逆矩阵的定义.................... 56
2.4.2 矩阵可逆的充要条件.......... 57
2.4.3 矩阵之间的等价关系.......... 59
2.4.4 解矩阵方程....................... 62
同步习题2.4................................ 64
2.5 矩阵的秩........................... 65
目 录
02
2 线性代数(慕课版)
2.5.1 矩阵秩的定义..................... 65
2.5.2 矩阵秩的性质.................... 66
2.5.3 矩阵秩的相关结论............. 68
同步习题2.5................................ 69
2.6 分块矩阵........................... 70
2.6.1 分块矩阵的定义................. 70
2.6.2 分块矩阵的运算................. 71
2.6.3 分块对角矩阵.................... 73
同步习题2.6................................ 76
2.7 运用MATLAB 进行矩阵
运算................................. 77
2.7.1 矩阵的加法........................ 77
2.7.2 矩阵的乘法、数乘、乘方... 78
2.7.3 求矩阵的转置.................... 78
2.7.4 求矩阵的逆....................... 78
2.7.5 求矩阵的行#简形.............. 79
第2 章思维导图..........................80
第2 章总复习题.......................... 81
03
第3 章 向量与向量
空间..............84
3.1 n 维向量及其线性运算........... 84
3.1.1 n 维向量的定义.................. 84
3.1.2 n 维向量的线性运算........... 85
同步习题3.1................................. 86
3.2 向量组的线性关系................ 86
3.2.1 向量组的线性组合.............. 86
3.2.2 向量组的等价.................... 87
3.2.3 线性组合的经济学应用
举例................................. 88
3.2.4 向量组线性相关性的
定义................................. 88
3.2.5 向量组线性相关性的
性质.................................90
3.2.6 向量组线性相关性的
判定................................. 92
同步习题3.2................................ 93
3.3 极大线性无关组和秩............. 95
3.3.1 极大线性无关组和向量组
的秩................................. 95
3.3.2 向量组的秩和矩阵的秩的
关系................................. 96
同步习题3.3................................98
3.4 向量空间........................... 99
3.4.1 向量空间的定义.................99
*3.4.2 过渡矩阵与坐标变换....... 100
同步习题3.4.............................. 102
3.5 向量的内积....................... 102
3.5.1 向量的内积的定义............ 102
3.5.2 向量组的正交规范化........ 104
3.5.3 正交矩阵......................... 105
同步习题3.5.............................. 106
3.6 运用MATLAB 解决向量
问题............................... 106
3.6.1 判断向量组的线性
相关性............................ 107
3.6.2 求极大无关组.................. 107
目录3
3.6.3 将向量组正交规范化........ 107
第3 章思维导图........................ 109
第3 章总复习题.........................110
04
第4 章 线性方程组....112
4.1 齐次线性方程组..................112
4.1.1 引例.................................112
4.1.2 齐次线性方程组解的性质....113
4.1.3 齐次线性方程组的
基础解系..........................113
同步习题4.1................................117
4.2 非齐次线性方程组...............119
4.2.1 非齐次线性方程组的基本
概念................................119
4.2.2 非齐次线性方程组解的
性质............................... 120
4.2.3 非齐次线性方程组的
解法............................... 120
同步习题4.2.............................. 125
4.3 线性方程组的应用.............. 127
4.3.1 向量组与线性方程组........ 127
4.3.2 利用线性方程组解的理论
求解线性方程组............... 129
4.3.3 矩阵方程与线性方程组..... 130
4.3.4 同解与公共解.................. 132
4.3.5 线性方程组应用案例........ 135
同步习题4.3.............................. 137
4.4 运用MATLAB 求解线性
方程组............................ 139
4.4.1 求解齐次线性方程组........ 139
4.4.2 求解非齐次线性方程组..... 139
第4 章思维导图.........................141
第4 章总复习题........................ 142
05
第5 章 矩阵的特征值与
特征向量...... 145
5.1 特征值与特征向量.............. 145
5.1.1 特征值与特征向量的
定义............................... 145
5.1.2 特征值与特征向量的
性质............................... 148
同步习题5.1................................151
5.2 相似矩阵......................... 152
5.2.1 相似矩阵的定义及性质..... 152
5.2.2 方阵的相似对角化........... 153
同步习题5.2.............................. 157
5.3 实对称矩阵及其对角化 ........ 159
5.3.1 实对称矩阵的特征值与特征
向量............................... 159
5.3.2 实对称矩阵的正交相似
对角化............................ 159
同步习题5.3.............................. 164
5.4 运用MATLAB 求解矩阵
问题............................... 165
4 线性代数(慕课版)
5.4.1 求特征值与特征向量......... 165
5.4.2 矩阵对角化的判断........... 166
第5 章思维导图........................ 168
第5 章总复习题........................ 169
06
第6 章 二次型..........171
6.1 二次型及其矩阵表示.............171
6.1.1 二次型的定义....................171
6.1.2 二次型及其矩阵............... 172
同步习题6.1............................... 173
6.2 二次型的标准形................. 174
6.2.1 利用正交变换法化二次型
为标准形......................... 174
6.2.2 利用配方法化二次型为
标准形............................ 177
同步习题6.2.............................. 178
6.3 正定二次型....................... 179
6.3.1 正定二次型的定义............ 179
6.3.2 赫尔维茨定理.................. 180
同步习题6.3...............................181
6.4 用MATLAB 进行二次型的
运算............................... 182
6.4.1 化二次型为标准形............ 182
6.4.2 正定二次型的判定........... 183
第6 章思维导图........................ 183
第6 章总复习题........................ 184
附录 线性代数中的数学
建模................ 186
参考答案 .................. 190
即时提问答案........................... 190
同步习题答案........................... 193
总复习题答案........................... 206
山东大学数学学院教授,泰山学堂主讲教师,山东数学会高等数学专业委员会主任,全国大学生数学竞赛山东赛区负责人,全国微课程比赛山东赛区副主任兼秘书长,中国大学先修课程《微积分》特聘教授。作为主要成员完成国家科学基金及山东省自然科学基金项目6项,主持或参与省部级教学研究项目5项;发表学术论文50余篇;参与编写的《微积分》入选国家十二五规划教材;曾获“山东省中青年学术骨干、学科带头人”等称号。

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