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

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