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线性代数简明教程/刘国庆 A CONCISE COURSE TO LINEAR ALGEBRA 版权信息
- ISBN：9787122345134
- 条形码：9787122345134 ; 978-7-122-34513-4
- 装帧：一般胶版纸
- 册数：暂无
- 重量：暂无
- 所属分类：>
线性代数简明教程/刘国庆 A CONCISE COURSE TO LINEAR ALGEBRA 本书特色
本书叙述深入浅出，以矩阵为主线，突出矩阵的运算和化简，突出用矩阵方法研究线性方程组、二次型和实际问题模型。本书对于抽象的理论和方法，总是从具体问题入手，再将其推广到一般情形，而略去了许多繁杂的理论推导，并力求将数学与应用相结合。
本书的主要内容包括线性方程组、矩阵代数、行列式、向量空间、矩阵的特征值与特征向量和二次型等。
本书是一本介绍性的线性代数教材，内容简洁，层次清晰，适合高等学校理工科专业线性代数课程双语教学使用。
本书叙述深入浅出，以矩阵为主线，突出矩阵的运算和化简，突出用矩阵方法研究线性方程组、二次型和实际问题模型。本书对于抽象的理论和方法，总是从具体问题入手，再将其推广到一般情形，而略去了许多繁杂的理论推导，并力求将数学与应用相结合。
本书的主要内容包括线性方程组、矩阵代数、行列式、向量空间、矩阵的特征值与特征向量和二次型等。
本书是一本介绍性的线性代数教材，内容简洁，层次清晰，适合高等学校理工科专业线性代数课程双语教学使用。
The matrix is the mainline of the book. With the help of the matrix operation
and the matrix simplification, we study the linear equations, the quadratic
forms and the real world applications. For the purpose of the insights into the
abstract theory and the methods of the linear algebra, we start to discuss the
conceptions and the methods with the specific problems, then we directly extend
them to the general situation without the complicated theoretical derivation.
Furthermore, we try to combine the mathematical methods with the real
applications in this book.
The main contents of the book are linear equations, matrix algebra,
determinants, vector spaces, eigenvalues and eigenvectors，and quadratic forms, etc.
线性代数简明教程/刘国庆 A CONCISE COURSE TO LINEAR ALGEBRA 内容简介
本书叙述深入浅出，以矩阵为主线，突出矩阵的运算和化简，突出用矩阵方法研究线性方程组、二次型和实际问题模型。本书对于抽象的理论和方法，总是从具体问题入手，再将其推广到一般情形，而略去了许多繁杂的理论推导，并力求将数学与应用相结合。 本书的主要内容包括线性方程组、矩阵代数、行列式、向量空间、矩阵的特征值与特征向量和二次型等。 本书是一本介绍性的线性代数教材，内容简洁，层次清晰，适合高等学校理工科专业线性代数课程双语教学使用。 The matrix is the mainline of the book. With the help of the matrix operation and the matrix simplification, we study the linear equations, the quadratic forms and the real world applications. For the purpose of the insights into the abstract theory and the methods of the linear algebra, we start to discuss the conceptions and the methods with the specific problems, then we directly extend them to the general situation without the complicated theoretical derivation. Furthermore, we try to combine the mathematical methods with the real applications in this book. The main contents of the book are linear equations, matrix algebra, determinants, vector spaces, eigenvalues and eigenvectors，and quadratic forms, etc.
线性代数简明教程/刘国庆 A CONCISE COURSE TO LINEAR ALGEBRA 目录
Chapter 1 Linear Equations in Linear
Algebra001
1.1Systems of Linear Equations001
1.2Row Reduction and Echelon Forms008
1.3Solutions of Linear Systems012
1.4Vector Equations014
Exercises017
Chapter 2 Matrix Algebra019
2.1Matrix Operations019
2.2The Inverse of a Matrix024
2.3Partitoned Matrices028
2.4Matrix Factorizations031
2.5Subspace of Rn032
2.6Dimension and Rank035
Exercises037
Chapter 3 Determinants040
3.1Introduction to Determinants040
3.2Properties of Determinants043
3.3Cofactor Expansion048
3.4The Inverse of a Matrix050
3.5Cramer’s Rule053
Exercises054
Chapter 4 Vector Spaces058
4.1Definition of Vector Spaces058
4.2Subspaces and Span062
4.3Linearly Independent Sets068
4.4Bases and Dimension071
4.5Inner Product，Length，Angle074
4.6Orthonormal Basis and the Gram-Schmidt Procedure078
Exercises084
Chapter 5 Eigenvalues and Eigenvectors088
5.1Definition of Eigenvalues and Eigenvectors088
5.2Properties of Eigenvalues and Eigenvectors092
5.3Similarity and Diagonalization096
5.4Diagonalization of Symmetric Matrices100
Exercises105
Chapter 6 Solution Sets of Linear Systems107
6.1Homogeneous Linear Systems107
6.2Solutions of Nonhomogeneous Systems108
6.3Applications of Linear Systems110
Exercises113
Chapter 7 Symmetric Matrices and Quadratic Forms117
7.1Diagonalization of Symmetric Matrices117
7.2Quadratic Forms119
7.3Quadratic Problems122
7.4The Singular Value Decomposition126
7.5Applications to Statistics129
Exercises132
References134
1.1Systems of Linear Equations001
1.2Row Reduction and Echelon Forms008
1.3Solutions of Linear Systems012
1.4Vector Equations014
Exercises017
Chapter 2 Matrix Algebra019
2.1Matrix Operations019
2.2The Inverse of a Matrix024
2.3Partitoned Matrices028
2.4Matrix Factorizations031
2.5Subspace of Rn032
2.6Dimension and Rank035
Exercises037
Chapter 3 Determinants040
3.1Introduction to Determinants040
3.2Properties of Determinants043
3.3Cofactor Expansion048
3.4The Inverse of a Matrix050
3.5Cramer’s Rule053
Exercises054
Chapter 4 Vector Spaces058
4.1Definition of Vector Spaces058
4.2Subspaces and Span062
4.3Linearly Independent Sets068
4.4Bases and Dimension071
4.5Inner Product，Length，Angle074
4.6Orthonormal Basis and the Gram-Schmidt Procedure078
Exercises084
Chapter 5 Eigenvalues and Eigenvectors088
5.1Definition of Eigenvalues and Eigenvectors088
5.2Properties of Eigenvalues and Eigenvectors092
5.3Similarity and Diagonalization096
5.4Diagonalization of Symmetric Matrices100
Exercises105
Chapter 6 Solution Sets of Linear Systems107
6.1Homogeneous Linear Systems107
6.2Solutions of Nonhomogeneous Systems108
6.3Applications of Linear Systems110
Exercises113
Chapter 7 Symmetric Matrices and Quadratic Forms117
7.1Diagonalization of Symmetric Matrices117
7.2Quadratic Forms119
7.3Quadratic Problems122
7.4The Singular Value Decomposition126
7.5Applications to Statistics129
Exercises132
References134
展开全部
线性代数简明教程/刘国庆 A CONCISE COURSE TO LINEAR ALGEBRA 作者简介
刘国庆，南京工业大学数理学院，教授，本人自从事科研工作以来一直致力于科学计算方面的研究，多年的研究已经取得了丰硕的成果。另外，本人多次赴美国大学进行访问，促使科研工作得到了极大的提升。教学方面，主要承担高等数学，线性代数，概率论，概率统计，数值分析，数学建模，数理方程和应用随机过程等主干课程的讲授任务，同时，已为学校留学生全英文主讲一轮《线性代数》课。
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