Andrilli/Hecker: Elementary Linear Algebra, 2nd Edition
Table of Contents
Preface
Prerequisite Chart
Applications Chart
Methods Chart
Chapter 1: Vectors and Matrices
Section 1.1: Fundamental Operations with Vectors
Section 1.2: The Dot Product
Section 1.3: An Introduction to Proofs
Section 1.4: Fundamental Operations with Matrices
Section 1.5: Matrix Multiplication
Chapter 2: Systems of Linear Equations
Section 2.1: Solving Systems of Linear Equations
Section 2.2: Equivalent Systems and Rank
Section 2.3: Row Space of a Matrix
Section 2.4: Inverses of Matrices
Chapter 3: Determinants and Eigenvalues
Section 3.1: Introduction to Determinants
Section 3.2: Determinants and Row Reduction
Section 3.3: Further Properties of the Determinant
Section 3.4: Eigenvalues and Diagonalization
Chapter 4: Finite Dimensional Vector Spaces
Section 4.1: Introduction to Vector Spaces
Section 4.2: Subspaces
Section 4.3: Span
Section 4.4: Linear Independence
Section 4.5: Basis and Dimension
Section 4.6: Constructing Special Bases
Section 4.7: Coordinatization
Chapter 5: Linear Transformations
Section 5.1: Introduction to Linear Transformations
Section 5.2: The Matrix of a Linear Transformation
Section 5.3: The Dimension Theorem
Section 5.4: Isomorphism
Section 5.5: Diagonalization of Linear Operators
Chapter 6: Orthogonality
Section 6.1: Orthogonal Bases and the Gram-Schmidt Process
Section 6.2: Orthogonal Complements
Section 6.3: Orthogonal Diagonalization
Chapter 7: Complex Vector Spaces and General Inner Products
Section 7.1: Complex Vector Spaces
Section 7.2: Inner Product Spaces
Chapter 8: Additional Applications
Section 8.1: Graph Theory (prerequisite: Section 1.5)
Section 8.2: Ohm’s Law (prerequisite: Section 2.1)
Section 8.3: Least-Squares Polynomials (prerequisite: Section 2.1)
Section 8.4: Markov Chains (prerequisite: Section 2.1)
Section 8.5: Hill Substitution: An Introduction to Coding Theory
(prerequisite: Section 2.4)
Section 8.6: Function Spaces (prerequisite: Section 4.7)
Section 8.7: Rotation of Axes (prerequisite: Section 4.7)
Section 8.8: Computer Graphics (prerequisite: Section 5.2)
Section 8.9: Differential Equations (prerequisite: Section 5.5)
Section 8.10: Least-Squares Solutions for Inconsistent Systems
(prerequisite: Section 6.2)
Section 8.11: Quadratic Forms (prerequisite: Section 6.3)
Chapter 9: Numerical Methods
Section 9.1: Numerical Methods for Solving Systems
(prerequisite: Section 2.2)
Section 9.2: LDU Decomposition (prerequisite: Section 2.4)
Section 9.3: The Power Method for Finding Eigenvalues
(prerequisite: Section 5.5)
Appendix A: Miscellaneous Proofs
Appendix B: Functions
Appendix C: Complex Numbers
Appendix D: Computers and Calculators
Appendix E: Answers to Selected Exercises
Subject Index