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Part-1 MATRICES AND LINEAR EQUATIONS 1. Arithmetic of Matrices 2. Elementary Matrices; Determinants 3. Vector Geometry in R^n Part-2 VECTOR SPACES 4. Vector Spaces 5. Subspaces 6. Linear Independence 7. Basis for a Vector Space Part-3 LINEAR MAPS BETWEEN VECTOR SPACES 8. Linearity 9. Linear Maps between Euclidean Spaces 10. Projection Operators Part-4 SPECTRAL THEORY OF VECTOR SPACES 11. Eigenvalues and Eigenvectors 12. Diagonalization of Matrices 13. Spectral Theorem for Vector Spaces 14. Some Applications of the Spectral Theorem 15. Every Operator is Diagonalizable Plus Nilpotent Part-5 THE GEOMETRY OF INNER PRODUCT SPACES 16. Complex Arithmetic 16.4 Answers to Odd-Numbered Exercises 17. Real and Complex Inner Product Spaces 18. Orthonormal Sets of Vectors 19. Quadratic Forms 20. Optimization Part-6 ADJOINT OPERATORS 21. Adjoints and Transposes 22. The Four Fundamental Subspaces 23. Orthogonal Projections 24. Least Squares Approximation Part-7 SPECTRAL THEORY OF INNER PRODUCT SPACES 25. Spectral Theorem for Real Inner Product Spaces 26. Spectral Theorem for Complex Inner Product Spaces
This book contains an extensive collection of exercises and problems that address relevant topics in linear algebra. The exercises will be both interesting and helpful to an average student. Topics that the author finds missing or inadequately covered in most existing books are also included. The exercises will be both interesting and helpful to an average student. Some are fairly routine calculations, while others require serious thought.The format of the questions makes them suitable for teachers to use in quizzes and assigned homework. Some of the problems may provide excellent topics for presentation and discussions. Furthermore, answers are given for all odd-numbered exercises which will be extremely useful for self-directed learners. In each chapter, there is a short background section which includes important definitions and statements of theorems to provide context for the following exercises and problems.
Title: Exercises and Problems in Linear Algebra by John Erdman Publisher: World Scientific Pub Co Inc Year: 2020 Pages: 220 Type: PDF Language: English ISBN-10 #: 9811220409 ISBN-13 #: 978-9811220401 License: GNU Amazon: Amazon
The author John M Erdman is Emeritus Associate Professor at Department of Mathematics and Statistics, Portland State University, Portland. His area of research interest is Functional Analysis and Operator Algebras.
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