Book:John B. Fraleigh/Linear Algebra/Third Edition

John B. Fraleigh and Raymond A. Beauregard: Linear Algebra (3rd Edition)

Published $\text {1995}$, Addison-Wesley Publishing Company,Inc.

ISBN 0-201-52675-1

Subject Matter

• Linear Algebra

Contents

Preface

Chapter 1 - Vectors, Matrices and Linear Systems

1.1 Vectors in Euclidean Spaces

1.2 The Norm and Dot Product

1.3 Matrices and Their Algebra

1.4 Solving Systems of Linear Equations

1.5 Inverses of Square Matrices

1.6 Homogeneous Systems, Subspaces and Bases

1.7 Application to Population Distribution (Optional)

1.8 Application to Binary Linear Codes

Chapter 2 - Dimension, Rank, and Linear Transformations

2.1 Independence and Dimension

2.2 The Rank of a Matrix

2.3 Linear Transformations of Euclidean Spaces

2.4 Linear Transformations of the Plane (Optional)

2.5 Lines, Planes and Other Flats (Optional)

Chapter 3 - Vector Spaces

3.1 Vector Spaces

3.2 Basic Concepts of Vector Spaces

3.3 Coordinatization of Vecotrs

3.4 Linear Transformatons

3.5 Inner-Product Spaces (Optional)

Chapter 4 - Determinants

4.1 Areas, Volumes and Cross Products

4.2 The Determinant of a Square Matrix

4.3 Computation of Determinants and Cramer's Rule

4.4 Linear Transformations and Determinants (Optional)

5 Eigenvalues and Eigenvectors

5.1 Eigenvalues and Eigenvectors

5.2 Diagonalization

5.3 Two Applications

Chapter 6 - Orthogonality

6.1 Projections

6.2 The Gram-Schmidt Process

6.3 Orthogonal Matrices

6.4 The Projection Matrix

6.5 The Method of Least Squares

Chapter 7 - Change of Basis

7.1 Coordinatization and Change of Basis

7.2 Matrix Representations and Similarity

Chapter 8 - Eigenvalues: Further Applications and Computations

8.1 Diagonalization of Quadratic orms

8.2 Applications to Geometry

8.3 Applications to Extrema

8.4 Computing Eigenvalues and Eigenvectors

Chapter 9 - Complex Scalars

9.1 Algebra of Complex Numbers

9.2 Matrices and Vector Spaces with Complex Scalars

9.3 Eigenvalues and Diagonalization

9.4 Jordan Canonical Form

Chapter 10 - Solving Large Linear Systems

10.1 Considerationso f Time

10.2 The $L U$-Factorization

10.3 Pivoting, Scaling, and Ill-Conditioned Matrices

Appendices

A Mathematical Induction

B Two Deferred Proofs

C Lintek Routines

D Matlab Procedures and Commands Used in the Exercises

Answers to Most Odd-Numbered Exercises

Index