# 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.

### 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
8.2 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