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Elementary Linear Algebra

6th Edition - April 5, 2022

Authors: Stephen Andrilli, David Hecker

Paperback ISBN:

9 7 8 - 0 - 1 2 - 8 2 2 9 7 8 - 1

eBook ISBN:

9 7 8 - 0 - 3 2 3 - 9 8 4 2 6 - 3

Elementary Linear Algebra, Sixth Edition provides a solid introduction to both the computational and theoretical aspects of linear algebra, covering many important real-world… Read more

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Elementary Linear Algebra, Sixth Edition provides a solid introduction to both the computational and theoretical aspects of linear algebra, covering many important real-world applications, including graph theory, circuit theory, Markov chains, elementary coding theory, least-squares polynomials and least-squares solutions for inconsistent systems, differential equations, computer graphics and quadratic forms. In addition, many computational techniques in linear algebra are presented, including iterative methods for solving linear systems, LDU Decomposition, the Power Method for finding eigenvalues, QR Decomposition, and Singular Value Decomposition and its usefulness in digital imaging.

Cover image
Title page
Table of Contents
Copyright
Dedication
Preface for the Instructor
Philosophy of the Text
Major Changes for the Sixth Edition
Plans for Coverage
Preface to the Student
A Light-Hearted Look at Linear Algebra Terms
Symbol Table
Computational & Numerical Techniques, Applications
Chapter 1: Vectors and Matrices
1.1. Fundamental Operations With Vectors
Exercises for Section 1.1
1.2. The Dot Product
Exercises for Section 1.2
1.3. An Introduction to Proof Techniques
Exercises for Section 1.3
1.4. Fundamental Operations With Matrices
Exercises for Section 1.4
1.5. Matrix Multiplication
Exercises for Section 1.5
Review Exercises for Chapter 1
Chapter 2: Systems of Linear Equations
2.1. Solving Linear Systems Using Gaussian Elimination
Exercises for Section 2.1
2.2. Gauss-Jordan Row Reduction and Reduced Row Echelon Form
Exercises for Section 2.2
2.3. Equivalent Systems, Rank, and Row Space
Exercises for Section 2.3
2.4. Inverses of Matrices
Exercises for Section 2.4
Review Exercises for Chapter 2
Chapter 3: Determinants and Eigenvalues
3.1. Introduction to Determinants
Exercises for Section 3.1
3.2. Determinants and Row Reduction
Exercises for Section 3.2
3.3. Further Properties of the Determinant
Exercises for Section 3.3
3.4. Eigenvalues and Diagonalization
Exercises for Section 3.4
Review Exercises for Chapter 3
Chapter 4: Finite Dimensional Vector Spaces
4.1. Introduction to Vector Spaces
Exercises for Section 4.1
4.2. Subspaces
Exercises for Section 4.2
4.3. Span
Exercises for Section 4.3
4.4. Linear Independence
Exercises for Section 4.4
4.5. Basis and Dimension
Exercises for Section 4.5
4.6. Constructing Special Bases
Exercises for Section 4.6
4.7. Coordinatization
Exercises for Section 4.7
Review Exercises for Chapter 4
Chapter 5: Linear Transformations
5.1. Introduction to Linear Transformations
Exercises for Section 5.1
5.2. The Matrix of a Linear Transformation
Exercises for Section 5.2
5.3. The Dimension Theorem
Exercises for Section 5.3
5.4. One-to-One and Onto Linear Transformations
Exercises for Section 5.4
5.5. Isomorphism
Exercises for Section 5.5
5.6. Diagonalization of Linear Operators
Exercises for Section 5.6
Review Exercises for Chapter 5
Chapter 6: Orthogonality
6.1. Orthogonal Bases and the Gram-Schmidt Process
Exercises for Section 6.1
6.2. Orthogonal Complements
Exercises for Section 6.2
6.3. Orthogonal Diagonalization
Exercises for Section 6.3
Review Exercises for Chapter 6
Chapter 7: Complex Vector Spaces and General Inner Products
7.1. Complex n-Vectors and Matrices
Exercises for Section 7.1
7.2. Complex Eigenvalues and Complex Eigenvectors
Exercises for Section 7.2
7.3. Complex Vector Spaces
Exercises for Section 7.3
7.4. Orthogonality in Cn
Exercises for Section 7.4
7.5. Inner Product Spaces
Exercises for Section 7.5
Review Exercises for Chapter 7
Chapter 8: Additional Applications
8.1. Graph Theory
Exercises for Section 8.1
8.2. Ohm's Law
Exercises for Section 8.2
8.3. Least-Squares Polynomials
Exercises for Section 8.3
8.4. Markov Chains
Exercises for Section 8.4
8.5. Hill Substitution: An Introduction to Coding Theory
Exercises for Section 8.5
8.6. Linear Recurrence Relations and the Fibonacci Sequence
Exercises for Section 8.6
8.7. Rotation of Axes for Conic Sections
Exercises for Section 8.7
8.8. Computer Graphics
Exercises for Section 8.8
8.9. Differential Equations
Exercises for Section 8.9
8.10. Least-Squares Solutions for Inconsistent Systems
Exercises for Section 8.10
8.11. Quadratic Forms
Exercises for Section 8.11
Chapter 9: Numerical Techniques
9.1. Numerical Techniques for Solving Systems
Exercises for Section 9.1
9.2. LDU Decomposition
Exercises for Section 9.2
9.3. The Power Method for Finding Eigenvalues
Exercises for Section 9.3
9.4. QR Factorization
Exercises for Section 9.4
9.5. Singular Value Decomposition
Exercises for Section 9.5
Appendix A: Miscellaneous Proofs
Appendix B: Functions
Exercises for Appendix B
Appendix C: Complex Numbers
Exercises for Appendix C
Appendix D: Elementary Matrices
Exercises for Appendix D
Appendix E: Answers to Selected Exercises
Index
Endpapers

Stephen Andrilli

Dr. Stephen Andrilli holds a Ph.D. degree in mathematics from Rutgers University, and is an Associate Professor in the Mathematics and Computer Science Department at La Salle University in Philadelphia, PA, having previously taught at Mount St. Mary’s University in Emmitsburg, MD. He has taught linear algebra to sophomore/junior mathematics, mathematics-education, chemistry, geology, and other science majors for over thirty years. Dr. Andrilli’s other mathematical interests include history of mathematics, college geometry, group theory, and mathematics-education, for which he served as a supervisor of undergraduate and graduate student-teachers for almost two decades. He has pioneered an Honors Course at La Salle based on Douglas Hofstadter’s “Godel, Escher, Bach,” into which he weaves the Alice books by Lewis Carroll. Dr. Andrilli lives in the suburbs of Philadelphia with his wife Ene. He enjoys travel, classical music, classic movies, classic literature, science-fiction, and mysteries. His favorite author is J. R. R. Tolkien.

Affiliations and expertise

LaSalle University, Philadelphia, PA, USA

David Hecker

Dr. David Hecker has a Ph.D. degree in mathematics from Rutgers University, and is a Professor in the Mathematics Department at Saint Joseph’s University in Philadelphia, PA. He has taught linear algebra to sophomore/junior mathematics and science majors for over three decades. Dr. Hecker has previously served two terms as Chair of his department, and his other mathematical interests include real and complex analysis, and linear algebra. He lives on five acres in the farmlands of New Jersey with his wife Lyn, and is very devoted to his four children. Dr. Hecker enjoys photography, camping and hiking, beekeeping, geocaching, science-fiction, humorous jokes and riddles, and rock and country music. His favorite rock group is the Moody Blues.

Affiliations and expertise

Professor, Mathematics Department, Saint Joseph's University, Philadelphia, PA, USA