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線性代數及其應用(第5版英文版)/高等學校教材系列

  • 作者:(美)戴維·C.萊//史蒂文·R.萊//朱迪·J.麥克唐納|責編:譚海平
  • 出版社:電子工業
  • ISBN:9787121396175
  • 出版日期:2020/09/01
  • 裝幀:平裝
  • 頁數:565
人民幣:RMB 99 元      售價:
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內容大鋼
    線性代數是處理矩陣和向量空間的數學分支科學,在現代數學的各個領域都有應用。本書內容主要包括線性代數中的線性方程、矩陣代數、行列式、向量空間、特徵值與特徵向量、正交性與最小二乘、對稱矩陣與二次型、向量空間解析幾何等,目的是讓學生掌握線性代數的基本概念、理論和證明。全書內容簡潔、例題豐富、版式美觀,除介紹基本概念外,還介紹了它們在各個領域中的具體應用。
    本書是一本介紹性的線性代數教材,內容翔實,層次清晰,適合作為高等學校理工科數學課程的雙語教學用書,也可作為公司職員及工程學研究人員的參考書。

作者介紹
(美)戴維·C.萊//史蒂文·R.萊//朱迪·J.麥克唐納|責編:譚海平

目錄
Preface
A Note to Students
Chapter 1  Linear Equations in Linear Algebra
  INTRODUCTORY EXAMPLE: Linear Models in Economics and Engineering
  1.1  Systems of Linear Equations
  1.2  Row Reduction and Echelon Forms
  1.3  Vector Equations
  1.4  The Matrix Equation Ax=b
  1.5  Solution Sets of Linear Systems
  1.6  Applications of Linear Systems
  1.7  Linear Independence
  1.8  Introduction to Linear Transformations
  1.9  The Matrix of a Linear Transformation
  1.10  Linear Models in Business, Science, and Engineering
  Supplementary Exercises
Chapter 2  Matrix Algebra
  INTRODUCTORY EXAMPLE: Computer Models in Aircraft Design
  2.1  Matrix Operations
  2.2  The Inverse of a Matrix
  2.3  Characterizations of Invertible Matrices
  2.4  Partitioned Matrices
  2.5  Matrix Factorizations
  2.6  The Leontief Input–Output Model
  2.7  Applications to Computer Graphics
  2.8  Subspaces of Rn
  2.9  Dimension and Rank
  Supplementary Exercises
Chapter 3   Determinants
  INTRODUCTORY EXAMPLE: Random Paths and Distortion
  3.1  Introduction to Determinants
  3.2  Properties of Determinants
  3.3  Cramer's Rule, Volume, and Linear Transformations
  Supplementary Exercises
Chapter 4  Vector Spaces
  INTRODUCTORY EXAMPLE: Space Flight and Control Systems
  4.1  Vector Spaces and Subspaces
  4.2  Null Spaces, Column Spaces, and Linear Transformations
  4.3  Linearly Independent Sets; Bases
  4.4  Coordinate Systems
  4.5  The Dimension of a Vector Space
  4.6  Rank
  4.7  Change of Basis
  4.8  Applications to Difference Equations
  4.9  Applications to Markov Chains
  Supplementary Exercises
Chapter 5  Eigenvalues and Eigenvectors
  INTRODUCTORY EXAMPLE: Dynamical Systems and Spotted Owls
  5.1  Eigenvectors and Eigenvalues
  5.2  The Characteristic Equation
  5.3  Diagonalization

  5.4  Eigenvectors and Linear Transformations
  5.5  Complex Eigenvalues
  5.6  Discrete Dynamical Systems
  5.7  Applications to Differential Equations
  5.8  Iterative Estimates for Eigenvalues
  Supplementary Exercises
Chapter 6  Orthogonality and Least Squares
  INTRODUCTORY EXAMPLE: The North American Datum and GPS Navigation
  6.1  Inner Product, Length, and Orthogonality
  6.2  Orthogonal Sets
  6.3  Orthogonal Projections
  6.4  The Gram-Schmidt Process
  6.5  Least-Squares Problems
  6.6  Applications to Linear Models
  6.7  Inner Product Spaces
  6.8  Applications of Inner Product Spaces
  Supplementary Exercises
Chapter 7  Symmetric Matrices and Quadratic Forms
  INTRODUCTORY EXAMPLE: Multichannel Image Processing
  7.1  Diagonalization of Symmetric Matrices
  7.2  Quadratic Forms
  7.3  Constrained Optimization
  7.4  The Singular Value Decomposition
  7.5  Applications to Image Processing and Statistics
  Supplementary Exercises
Chapter 8  The Geometry of Vector Spaces
  INTRODUCTORY EXAMPLE: The Platonic Solids
  8.1  Affine Combinations
  8.2  Affine Independence
  8.3  Convex Combinations
  8.4  Hyperplanes
  8.5  Polytopes
  8.6  Curves and Surfaces
Chapter 9  Optimization (Online)
  INTRODUCTORY EXAMPLE: The Berlin Airlift
  9.1  Matrix Games
  9.2  Linear Programming—Geometric Method
  9.3  Linear Programming—Simplex Method
  9.4  Duality
Chapter 10  Finite-State Markov Chains (Online)
  INTRODUCTORY EXAMPLE: Googling Markov Chains
  10.1  Introduction and Examples
  10.2  The Steady-State Vector and Google's PageRank
  10.3  Communication Classes
  10.4  Classification of States and Periodicity
  10.5  The Fundamental Matrix
  10.6  Markov Chains and Baseball Statistics
Appendixes
  A  Uniqueness of the Reduced Echelon Form
  B  Complex Numbers

Glossary
Answers to Odd-Numbered Exercises

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