LINEAR ALGEBRA/孙晓娟
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作者孙晓娟编著
出版社北京邮电大学出版社
ISBN9787563555925
出版时间2018-09
装帧平装
开本16开
定价28元
货号1201781800
上书时间2024-09-03
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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 Laplaces 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 o{
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
内容摘要
孙晓娟编著的《线性代数(普通高等教育十三五规划教材)(英文版)》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。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；很后，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。
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