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Elementary Linear Algebra, Applications Version

Elementary Linear Algebra, Applications Version 11th Edition

By: Howard Anton, Chris Rorres
ISBN-10: 1118434412
/ ISBN-13: 9781118878767
Edition: 11th Edition
Language: English
				
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Title Page

Copyright Page

About the Author

Dedication

Preface

CONTENTS

CHAPTER 1 Systems of Linear Equations and Matrices

    • 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
    • 1.6 More on Linear Systems and Invertible Matrices
    • 1.7 Diagonal, Triangular, and Symmetric Matrices
    • 1.8 Matrix Transformations
    • 1.9 Applications of Linear Systems
    • Network Analysis (Traffic Flow)
    • Electrical Circuits
    • Balancing Chemical Equations
    • Polynomial Interpolation
    • 1.10 Application: Leontief Input-Output Models

CHAPTER 2 Determinants

    • 2.1 Determinants by Cofactor Expansion
    • 2.2 Evaluating Determinants by Row Reduction
    • 2.3 Properties of Determinants; Cramer’s Rule

CHAPTER 3 Euclidean Vector Spaces

    • 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 4 General Vector Spaces

    • 4.1 Real Vector Spaces
    • 4.2 Subspaces
    • 4.3 Linear Independence
    • 4.4 Coordinates and Basis
    • 4.5 Dimension
    • 4.6 Change of Basis
    • 4.7 Row Space, Column Space, and Null Space
    • 4.8 Rank, Nullity, and the Fundamental Matrix Spaces
    • 4.9 Basic Matrix Transformations in R2 and R3
    • 4.10 Properties of Matrix Transformations
    • 4.11 Application: Geometry of Matrix Operators on R2

CHAPTER 5 Eigenvalues and Eigenvectors

    • 5.1 Eigenvalues and Eigenvectors
    • 5.2 Diagonalization
    • 5.3 Complex Vector Spaces
    • 5.4 Application: Differential Equations
    • 5.5 Application: Dynamical Systems and Markov Chains

CHAPTER 6 Inner Product Spaces

    • 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 Application: Mathematical Modeling Using Least Squares
    • 6.6 Application: Function Approximation; Fourier Series

CHAPTER 7 Diagonalization and Quadratic Forms

    • 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 8 General Linear Transformations

    • 8.1 General Linear Transformations
    • 8.2 Compositions and Inverse Transformations
    • 8.3 Isomorphism
    • 8.4 Matrices for General Linear Transformations
    • 8.5 Similarity

CHAPTER 9 Numerical Methods

    • 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 Application: Data Compression Using Singular Value Decomposition

CHAPTER 10 Applications of Linear Algebra

    • 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 Leontief Economic Models
    • 10.8 Forest Management
    • 10.9 Computer Graphics
    • 10.10 Equilibrium Temperature Distributions
    • 10.11 Computed Tomography
    • 10.12 Fractals
    • 10.13 Chaos
    • 10.14 Cryptography
    • 10.15 Genetics
    • 10.16 Age-Specific Population Growth
    • 10.17 Harvesting of Animal Populations
    • 10.18 A Least Squares Model for Human Hearing
    • 10.19 Warps and Morphs
    • 10.20 Internet Search Engines

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