书籍详情
LINEAR ALGEBRA
作者：孙晓娟
出版社：北京邮电大学出版社
出版时间：2018-09-01
ISBN：9787563555925
定价：¥28.00
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内容简介
《LINEAR ALGEBRA（线性代数 英文版）/普通高等教育“十三五”规划教材》的主要内容是矩阵和行列式、线性方程组、方阵的特征值和特征向量、二次型，共四个章节。第1章先引入矩阵的概念，而后介绍矩阵的基本运算和性质、矩阵的秩和逆、方阵的行列式运算及其性质；第2章介绍线性方程组的解、向量组的线性相关性、正交基；第3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4章介绍二次型及其矩阵和将二次型化为标准型的方法。
作者简介
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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
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