- 北京邮电大学出版社
- 9787563555925
- 226270
- 48255163-7
- 2018-09
- 理学
- 数学
- O151.2
- 通用
- 本科 高职 五年制高职 高职本科（应用型本科） 中职
内容简介
《Linear Algebra》（留学生英文教材）的主要内容是矩阵、行列式、线性方程组、方阵的特征值和特征向量、二次型共五个章节。先引入矩阵的概念，而后介绍矩阵的基本运算和性质，矩阵的秩和逆；在矩阵的基础上，第二章介绍方阵的行列式运算以及行列式的性质及计算；第三章介绍线性方程组的解及向量组的相关性；第四章介绍方阵的特征值与特征向量，以及方阵的相似对角化；最后第五章介绍二次型及其矩阵和将二次型化为标准型的方法。
目录
Chapter 1 Matrices and Determinants
1．1 Matrices
1．2 Matrix Arithmetic
1．2．1 Equality
1．2．2 Scalar Multiplication
1．2．3 Matrix Addition
1．2．4 Matrix Multiplication
1．2．5 Transpose of a Matrix
1．3 Determinants of Square Matrices
1．3．1 Second Order Determinant
1．3．2 n-th Order Determinant
1．3．3 Properties of Determinants
1．3．4 Evaluation of Determinants
1．3．5 Laplace's Theorem
1．4 Block Matrices
1．4．1 The Concept of Block Matrices
1．4．2 Evaluation of Block Matrices
1．5 Invertible Matrices
1．6 Elementary Matrices
1．6．1 Elementary Operations of Matrices
1．6．2 Elementary Matrices
1．6．3 Use Elementary Operations to Get the Inverse Matrix
1．7 Rank of Matrices
1．8 Exercises
Chapter 2 Systems of Linear Equations
2．1 Systems of Linear Equations
2．2 Vectors
2．3 Linear Independence
2．3．1 Linear Combination
2．3．2 Linear Dependence and Linear Independence
2．4 Maximally Linearly Independent Vector Group
2．4．1 Equivalent Vector Sets
2．4．2 Maximally Linearly Independent Group
2．4．3 The Relationship Between Rank of Matrices and Rank of Vector Sets
2．5 Vector Space
2．6 General Solutions of Linear Systems
2．6．1 General Solutions of Homogenous Linear Systems
2．6．2 General Solutions of Non-homogenous Linear Systems
2．7 Exercises
Chapter 3 Eigenvalues and Eigenveetors
3．1 Eigenvalues and Eigenvectors
3．1．1 Definition of Eigenvalues and Eigenvectors
3．1．2 Properties of Eigenvalues and Eigenvectors
3．2 Diagonalization o{ Square Matrices
3．2．1 Similar Matrix
3．2．2 Diagonalization of Square Matrices
3．3 Orthonormal Basis
3．3．1 Inner Product of Vectors
3．3．2 Orthogonal Set and Basis
3．3．3 Gram-Schmidt Orthogonalization Process
3．3．4 Orthogonal Matrix
3．4 Diagonalization of Real Symmetric Matrices
3．4．1 Properties of Eigenvalues of Real Symmetric Matrices
3．5 Exercises
Chapter 4 Quadratic Form
4．1 Real Quadratic Form and Its Matrix
4．2 Diagonal Form of Quadratic Form
4．3 Diagonal Form of Real Quadratic Form
4．3．1 Changing Quadratic Form into Diagonal Form by Orthogonal Transformation
4．3．2 Changing Quadratic Form into Diagonal Form by the Method of Completing the Square
4．4 Canonical Form of Real Quadratic Form
4．5 Positive Definite Quadratic Form and Matrices
4．6 Exercises
References
1．1 Matrices
1．2 Matrix Arithmetic
1．2．1 Equality
1．2．2 Scalar Multiplication
1．2．3 Matrix Addition
1．2．4 Matrix Multiplication
1．2．5 Transpose of a Matrix
1．3 Determinants of Square Matrices
1．3．1 Second Order Determinant
1．3．2 n-th Order Determinant
1．3．3 Properties of Determinants
1．3．4 Evaluation of Determinants
1．3．5 Laplace's Theorem
1．4 Block Matrices
1．4．1 The Concept of Block Matrices
1．4．2 Evaluation of Block Matrices
1．5 Invertible Matrices
1．6 Elementary Matrices
1．6．1 Elementary Operations of Matrices
1．6．2 Elementary Matrices
1．6．3 Use Elementary Operations to Get the Inverse Matrix
1．7 Rank of Matrices
1．8 Exercises
Chapter 2 Systems of Linear Equations
2．1 Systems of Linear Equations
2．2 Vectors
2．3 Linear Independence
2．3．1 Linear Combination
2．3．2 Linear Dependence and Linear Independence
2．4 Maximally Linearly Independent Vector Group
2．4．1 Equivalent Vector Sets
2．4．2 Maximally Linearly Independent Group
2．4．3 The Relationship Between Rank of Matrices and Rank of Vector Sets
2．5 Vector Space
2．6 General Solutions of Linear Systems
2．6．1 General Solutions of Homogenous Linear Systems
2．6．2 General Solutions of Non-homogenous Linear Systems
2．7 Exercises
Chapter 3 Eigenvalues and Eigenveetors
3．1 Eigenvalues and Eigenvectors
3．1．1 Definition of Eigenvalues and Eigenvectors
3．1．2 Properties of Eigenvalues and Eigenvectors
3．2 Diagonalization o{ Square Matrices
3．2．1 Similar Matrix
3．2．2 Diagonalization of Square Matrices
3．3 Orthonormal Basis
3．3．1 Inner Product of Vectors
3．3．2 Orthogonal Set and Basis
3．3．3 Gram-Schmidt Orthogonalization Process
3．3．4 Orthogonal Matrix
3．4 Diagonalization of Real Symmetric Matrices
3．4．1 Properties of Eigenvalues of Real Symmetric Matrices
3．5 Exercises
Chapter 4 Quadratic Form
4．1 Real Quadratic Form and Its Matrix
4．2 Diagonal Form of Quadratic Form
4．3 Diagonal Form of Real Quadratic Form
4．3．1 Changing Quadratic Form into Diagonal Form by Orthogonal Transformation
4．3．2 Changing Quadratic Form into Diagonal Form by the Method of Completing the Square
4．4 Canonical Form of Real Quadratic Form
4．5 Positive Definite Quadratic Form and Matrices
4．6 Exercises
References
