Elementary Linear Algebra
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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 realworld applications, including graph theory, circuit theory, Markov chains, elementary coding theory, leastsquares polynomials and leastsquares 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.
Key Features

Prepares students with a thorough coverage of the fundamentals of introductory linear algebra

Presents each chapter as a coherent, organized theme, with clear explanations for each new concept

Builds a foundation for math majors in the reading and writing of elementary mathematical proofs"
Readership
Students at the advanced undergraduate level, Researchers/Professionals
Table of Contents
 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 LightHearted 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. GaussJordan 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. OnetoOne 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 GramSchmidt 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 nVectors 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. LeastSquares 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. LeastSquares 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
Product details
 No. of pages: 544
 Language: English
 Copyright: © Academic Press 2022
 Published: April 5, 2022
 Imprint: Academic Press
 Paperback ISBN: 9780128229781
 eBook ISBN: 9780323984263
About the Authors
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, mathematicseducation, 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 mathematicseducation, for which he served as a supervisor of undergraduate and graduate studentteachers 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, sciencefiction, 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, sciencefiction, 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