Linear Algebra: An Introduction, Second Edition

Book PDF Download

Table of Contents

Linear Algebra


Chapter 1: Matrices

1.1 Basic Concepts

1.2 Matrix Multiplication

1.3 Special Matrices

1.4 Linear Systems of Equations

1.5 The Inverse

1.6 LU Decomposition

1.7 Properties of Rn

Chapter 1 Review

Chapter 2: Vector Spaces

2.1 Vectors

2.2 Subspaces

2.3 Linear Independence

2.4 Basis and Dimension

2.5 Row Space of a Matrix

2.6 Rank of a Matrix

Chapter 2 Review

Chapter 3: Linear Transformations

3.1 Functions

3.2 Linear Transformations

3.3 Matrix Representations

3.4 Change of Basis

3.5 Properties of Linear Transformations

Chapter 3 Review

Chapter 4: Eigenvalues, Eigenvectors, and Differential Equations

4.1 Eigenvectors and Eigenvalues

4.2 Properties of Eigenvalues and Eigenvectors

4.3 Diagonalization of Matrices

4.4 The Exponential Matrix

4.5 Power Methods

4.6 Differential Equations in Fundamental Form

4.7 Solving Differential Equations in Fundamental Form

4.8 A Modeling Problem

Chapter 4 Review

Chapter 5: Euclidean Inner Product

5.1 Orthogonality

5.2 Projections

5.3 The QR Algorithm

5.4 Least Squares

5.5 Orthogonal Complements

Chapter 5 Review

Appendix A: Determinants

Appendix B: Jordan Canonical Forms

Appendix C: Markov Chains

Appendix D: The Simplex Method: An Example

Appendix E: A Word on Numerical Techniques and Technology

Answers and Hints to Seclected Problems

Chapter 1

Chapter 2

Chapter 3

Chapter 4

Chapter 5

Appendix A

Appendix B

Appendix C

Appendix D


An eet,


Richard Bronson
Gabriel B. Costa