线性代数(第6版)(英文版)9787302668077
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作者(美)吉尔伯特·斯特朗|
出版社清华大学
ISBN9787302668077
出版时间2024-07
装帧平装
开本其他
定价108元
货号32170280
上书时间2024-12-15
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作者简介
William Gilbert Strang（威廉·吉尔伯特·斯特朗），1934年11月27日于芝加哥出生，是美国享有盛誉的数学家，在有限元理论、变分法、小波分析及线性代数方面均有所建树。他对教育的贡献尤为卓著，包括所著有的七部经典数学教材及一部专著。斯特朗自1962年担任麻省理工学院教授，其所授课程《线性代数导论》、《计算科学与工程》均在麻省理工学院开放式课程计划（MIT Open Course Ware）中收录，并获得广泛好评。
目录
1 Vectors and Matrices
1.1 Vectors and Linear Combinations
1.2 Lengths and Angles from Dot Products
1.3 Matrices and Their Column Spaces
1.4 Matrix Multiplication AB and CR
2 Solving Linear Equations Ax=b
2.1 Elimination and Back Substitution
2.2 Elimination Matrices and Inverse Matrices
2.3 Matrix Computations and A=LU
2.4 Permutations and Transposes
2.5 Derivatives and Finite Difference Matrices
3 The Four Fundamental Subspaces
3.1 Vector Spaces and Subspaces
3.2 Computing the Nullspace by Elimination: A=CR
3.3 The Complete Solution to Ax=b
3.4 Independence, Basis, and Dimension
3.5 Dimensions of the Four Subspaces
4 Orthogonality
4.1 Orthogonality of Vectors and Subspaces
4.2 Projections onto Lines and Subspaces
4.3 Least Squares Approximations
4.4 Orthonormal Bases and Gram-Schmidt
4.5 The Pseudoinverse of a Matrix
5 Determinants
5.1 3 by 3 Determinants and Cofactors
5.2 Computing and Using Determinants
5.3 Areas and Volumes by Determinants
6 Eigenvalues and Eigenvectors
6.1 Introduction to Eigenvalues: Ax=Xx
6.2 Diagonalizing a Matrix
6.3 Symmetric Positive Definite Matrices
6.4 Complex Numbers and Vectors and Matrices
6.5 Solving Linear Differential Equations
7 The Singular Value Decomposition (SVD)
7.1 Singular Values and Singular Vectors
7.2 Image Processing by Lincar Algebra
7.3 Principal Component Analysis (PCA by the SVD)
8 Linear Transformations
8.1 The Idea of a Linear Transformation
8.2 The Matrix of a Linear Transformation
8.3 The Search for a Good Basis
9 Linear Algebra in Optimization
9.1 Minimizing a Multivariable Function
9.2 Backpropagation and Stochastic Gradient Descent
9.3 Constraints, Lagrange Multipliers, Minimum Norms
9.4 Linear Programming, Game Theory, and Duality
10 Learning from Data
10.1 Piecewise Linear Learning Functions
10.2 Creating and Experimenting
10.3 Mean, Variance, and Covariance
Appendix 1 The Ranks of AB and A+ B due i
Appendix 2 Matrix Factorizations
Appendix 3 Counting Parameters in the Basic Factorizations
Appendix 4 Codes and Algorithms for Numerical Linear Algebra
Appendix 5 The Jordan Form of a Square Matrix
Appendix 6 Tensors
Appendix 7 The Condition Number of a Matrix Problem
Appendix 8 Markov Matrices and Perron-Frobenius
Appendix 9 Elimination and Factorization
Appendix 10 Computer Graphics
Index of Equations
Index of Notations
Index
内容摘要
本书内容包括行列式、
矩阵、线性方程组与向量、
矩阵的特征值与特征向量、
二次型及Mathematica软件的应用等。每章都配有习题，书后给出了习题答案。本书在编写中力求重点突出、
由浅入深、通俗易懂，努力体现教学的适用性。本书可作为高等院校工科专业的学生的教材，也可作为其他非数学类本科专业学生的教材或教学参考书
主编推荐
Gilbert Strang的《线性代数（第5版）》是一本经典线性代数教材。此书深入浅出地展示了线性代数的所有核心概念，讲述过程中恰当穿插了各种应用，体现了线性代数极端有用的思想。
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