線性代數 (第6版)-英文 吉爾伯特.斯特朗 9787302668077 【台灣高等教育出版社】

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物品所在地:中國大陸
原出版社:清華大學
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書名:線性代數 (第6版)-英文
ISBN:9787302668077
出版社:清華大學
著編譯者:吉爾伯特.斯特朗
頁數:430
所在地:中國大陸 *此為代購商品
書號:1675586
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內容簡介

本書內容包括行列式、矩陣、線性方程組與向量、矩陣的特徵值與特徵向量、二次型及Mathematica軟體的應用等。每章都配有習題,書後給出了習題答案。本書在編寫中力求重點突出、由淺入深、通俗易懂,努力體現教學的適用性。本書可作為高等院校工科專業的學生的教材,也可作為其他非數學類本科專業學生的教材或教學參考書

目錄

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

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