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 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.
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 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
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, 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