**Elementary Linear Algebra: Applications Version 12th Edition by Howard Anton, ISBN-13: 978-1119406723**

[PDF eBook eTextbook]

- Publisher: Wiley; 12th edition (February 20, 2019)
- Language: English
- 800 pages
- ISBN-10: 9781119406723

- ISBN-13: 978-1119406723

* Elementary Linear Algebra: Applications Version, 12th Edition* gives an elementary treatment of linear algebra that is suitable for a first course for undergraduate students. The aim is to present the fundamentals of linear algebra in the clearest possible way; pedagogy is the main consideration. Calculus is not a prerequisite, but there are clearly labeled exercises and examples (which can be omitted without loss of continuity) for students who have studied calculus.

**Table of Contents:**

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

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