Exercises and Problems in Linear Algebra

✍ Scribed by John M. Erdman

• Publisher: World Scientific Publishing Company
• Year: 2020
• Tongue: English
• Leaves: 220
• Category: Library

✦ Synopsis

This book contains an extensive collection of exercises and problems that address relevant topics in linear algebra. 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.

✦ Table of Contents

Contents
Preface
Part 1. MATRICES AND LINEAR EQUATIONS
Chapter 1. Arithmetic of Matrices
1.1 Background
1.2 Exercises
1.3 Problems
1.4 Answers to Odd-Numbered Exercises
Chapter 2. Elementary Matrices; Determinants
2.1 Background
2.2 Exercises
2.3 Problems
2.4 Answers to Odd-Numbered Exercises
Chapter 3. Vector Geometry in R^n
3.1 Background
3.2 Exercises
3.3 Problems
3.4 Answers to Odd-Numbered Exercises
Part 2. VECTOR SPACES
Chapter 4. Vector Spaces
4.1 Background
4.2 Exercises
4.3 Problems
4.4 Answers to Odd-Numbered Exercises
Chapter 5. Subspaces
5.1 Background
5.2 Exercises
5.3 Problems
5.4 Answers to Odd-Numbered Exercises
Chapter 6. Linear Independence
6.1 Background
6.2 Exercises
6.3 Problems
6.4 Answers to Odd-Numbered Exercises
Chapter 7. Basis for a Vector Space
7.1 Background
7.2 Exercises
7.3 Problems
7.4 Answers to Odd-Numbered Exercises
Part 3. LINEAR MAPS BETWEEN VECTOR SPACES
Chapter 8. Linearity
8.1 Background
8.2 Exercises
8.3 Problems
8.4 Answers to Odd-Numbered Exercises
Chapter 9. Linear Maps between Euclidean Spaces
9.1 Background
9.2 Exercises
9.3 Problems
9.4 Answers to Odd-Numbered Exercises
Chapter 10. Projection Operators
10.1 Background
10.2 Exercises
10.3 Problems
10.4 Answers to Odd-Numbered Exercises
Part 4. SPECTRAL THEORY OF VECTOR SPACES
Chapter 11. Eigenvalues and Eigenvectors
11.1 Background
11.2 Exercises
11.3 Problems
11.4 Answers to Odd-Numbered Exercises
Chapter 12. Diagonalization of Matrices
12.1 Background
12.2 Exercises
12.3 Problems
12.4 Answers to Odd-Numbered Exercises
Chapter 13. Spectral Theorem for Vector Spaces
13.1 Background
13.2 Exercises
13.3 Problem
13.4 Answers to Odd-Numbered Exercises
Chapter 14. Some Applications of the Spectral Theorem
14.1 Background
14.2 Exercises
14.3 Problems
14.4 Answers to Odd-Numbered Exercises
Chapter 15. Every Operator is Diagonalizable Plus Nilpotent
15.1 Background
15.2 Exercises
15.3 Problems
15.4 Answers to Odd-Numbered Exercises
Part 5. THE GEOMETRY OF INNER PRODUCT SPACES
Chapter 16. Complex Arithmetic
16.1 Background
16.2 Exercises
16.3 Problems
16.4 Answers to Odd-Numbered Exercises
Chapter 17. Real and Complex Inner Product Spaces
17.1 Background
17.2 Exercises
17.3 Problems
17.4 Answers to Odd-Numbered Exercises
Chapter 18. Orthonormal Sets of Vectors
18.1 Background
18.2 Exercises
18.3 Problems
18.4 Answers to Odd-Numbered Exercises
Chapter 19. Quadratic Forms
19.1 Background
19.2 Exercises
19.3 Problem
19.4 Answers to Odd-Numbered Exercises
Chapter 20. Optimization
20.1 Background
20.2 Exercises
20.3 Problems
20.4 Answers to Odd-Numbered Exercises
Part 6. ADJOINT OPERATORS
Chapter 21. Adjoints and Transposes
21.1 Background
21.2 Exercises
21.3 Problems
21.4 Answers to Odd-Numbered Exercises
Chapter 22. The Four Fundamental Subspaces
22.1 Background
22.2 Exercises
22.3 Problems
22.4 Answers to Odd-Numbered Exercises
Chapter 23. Orthogonal Projections
23.1 Background
23.2 Exercises
23.3 Problems
23.4 Answers to Odd-Numbered Exercises
Chapter 24. Least Squares Approximation
24.1 Background
24.2 Exercises
24.3 Problems
24.4 Answers to Odd-Numbered Exercises
Part 7. SPECTRAL THEORY OF INNER PRODUCT SPACES
Chapter 25. Spectral Theorem for Real Inner Product Spaces
25.1 Background
25.2 Exercises
25.3 Problem
25.4 Answers to the Odd-Numbered Exercises
Chapter 26. Spectral Theorem for Complex Inner Product Spaces
26.1 Background
26.2 Exercises
26.3 Problems
26.4 Answers to Odd-Numbered Exercises
BIBLIOGRAPHY
INDEX