Efnisyfirlit

• Cover
• Table of Contents
• Applications and Historical Topics
• Title Page
• Copyright
• Dedication
• About the Authors
• Preface
• CHAPTER 1: Systems of Linear Equations and Matrices
• CHAPTER CONTENTS
• Introduction
• 1.1 Introduction to Systems of Linear Equations
• 1.2 Gaussian Elimination
• 1.3 Matrices and Matrix Operations
• 1.4 Inverses; Algebraic Properties of Matrices
• 1.5 Elementary Matrices and a Method for Finding A
• 1.6 More on Linear Systems and Invertible Matrices
• 1.7 Diagonal, Triangular, and Symmetric Matrices
• 1.8 Introduction to Linear Transformations
• 1.9 Compositions of Matrix Transformations
• 1.10 Applications of Linear Systems
• 1.11 Leontief Input‐Output Models
• Chapter 1 Supplementary Exercises
• CHAPTER 2: Determinants
• CHAPTER CONTENTS
• Introduction
• 2.1 Determinants by Cofactor Expansion
• 2.2 Evaluating Determinants by Row Reduction
• 2.3 Properties of Determinants; Cramer’s Rule
• Chapter 2 Supplementary Exercises
• CHAPTER 3: Euclidean Vector Spaces
• CHAPTER CONTENTS
• Introduction
• 3.1 Vectors in 2‐Space, 3‐Space, and n‐Space
• 3.2 Norm, Dot Product, and Distance in Rn
• 3.3 Orthogonality
• 3.4 The Geometry of Linear Systems
• 3.5 Cross Product
• Chapter 3 Supplementary Exercises
• CHAPTER 4: General Vector Spaces
• CHAPTER CONTENTS
• Introduction
• 4.1 Real Vector Spaces
• 4.2 Subspaces
• 4.3 Spanning Sets
• 4.4 Linear Independence
• 4.5 Coordinates and Basis
• 4.6 Dimension
• 4.7 Change of Basis
• 4.8 Row Space, Column Space, and Null Space
• 4.9 Rank, Nullity, and the Fundamental Matrix Spaces
• Chapter 4 Supplementary Exercises
• CHAPTER 5: Eigenvalues and Eigenvectors
• CHAPTER CONTENTS
• Introduction
• 5.1 Eigenvalues and Eigenvectors
• 5.2 Diagonalization
• 5.3 Complex Vector Spaces
• 5.4 Differential Equations
• 5.5 Dynamical Systems and Markov Chains
• Chapter 5 Supplementary Exercises
• CHAPTER 6: Inner Product Spaces
• CHAPTER CONTENTS
• Introduction
• 6.1 Inner Products
• 6.2 Angle and Orthogonality in Inner Product Spaces
• 6.3 Gram–Schmidt Process; QR‐Decomposition
• 6.4 Best Approximation; Least Squares
• 6.5 Mathematical Modeling Using Least Squares
• 6.6 Function Approximation; Fourier Series
• Chapter 6 Supplementary Exercises
• CHAPTER 7: Diagonalization and Quadratic Forms
• CHAPTER CONTENTS
• Introduction
• 7.1 Orthogonal Matrices
• 7.2 Orthogonal Diagonalization
• 7.3 Quadratic Forms
• 7.4 Optimization Using Quadratic Forms
• 7.5 Hermitian, Unitary, and Normal Matrices
• Chapter 7 Supplementary Exercises
• CHAPTER 8: General Linear Transformations
• CHAPTER CONTENTS
• Introduction
• 8.1 General Linear Transformations
• 8.2 Compositions and Inverse Transformations
• 8.3 Isomorphism
• 8.4 Matrices for General Linear Transformations
• 8.5 Similarity
• 8.6 Geometry of Matrix Operators
• Chapter 8 Supplementary Exercises
• CHAPTER 9: Numerical Methods
• CHAPTER CONTENTS
• Introduction
• 9.1 LU‐Decompositions
• 9.2 The Power Method
• 9.3 Comparison of Procedures for Solving Linear Systems
• 9.4 Singular Value Decomposition
• 9.5 Data Compression Using Singular Value Decomposition
• Chapter 9 Supplementary Exercises
• CHAPTER 10: Applications of Linear Algebra
• CHAPTER CONTENTS
• Introduction
• 10.1 Constructing Curves and Surfaces Through Specified Points
• 10.2 The Earliest Applications of Linear Algebra
• 10.3 Cubic Spline Interpolation
• 10.4 Markov Chains
• 10.5 Graph Theory
• 10.6 Games of Strategy
• 10.7 Forest Management
• 10.8 Computer Graphics
• 10.9 Equilibrium Temperature Distributions
• 10.10 Computed Tomography
• 10.11 Fractals
• 10.12 Chaos
• 10.13 Cryptography
• 10.14 Genetics
• 10.15 Age‐Specific Population Growth
• 10.16 Harvesting of Animal Populations
• 10.17 A Least Squares Model for Human Hearing
• 10.18 Warps and Morphs
• 10.19 Internet Search Engines
• 10.20 Facial Recognition
• Appendix A: Working with Proofs
• Appendix B: Complex Numbers
• Index
• End User License Agreement