Exercises and problems in linear algebra

PREFACE
Part 1. MATRICES AND LINEAR EQUATIONS
	Chapter 1. SYSTEMS OF LINEAR EQUATIONS
		1.1. Background
		1.2. Exercises
		1.3. Problems
		1.4. Answers to Odd-Numbered Exercises
	Chapter 2. ARITHMETIC OF MATRICES
		2.1. Background
		2.2. Exercises
		2.3. Problems
		2.4. Answers to Odd-Numbered Exercises
	Chapter 3. ELEMENTARY MATRICES; DETERMINANTS
		3.1. Background
		3.2. Exercises
		3.3. Problems
		3.4. Answers to Odd-Numbered Exercises
	Chapter 4. VECTOR GEOMETRY IN Rn
		4.1. Background
		4.2. Exercises
		4.3. Problems
		4.4. Answers to Odd-Numbered Exercises
Part 2. VECTOR SPACES
	Chapter 5. VECTOR SPACES
		5.1. Background
		5.2. Exercises
		5.3. Problems
		5.4. Answers to Odd-Numbered Exercises
	Chapter 6. SUBSPACES
		6.1. Background
		6.2. Exercises
		6.3. Problems
		6.4. Answers to Odd-Numbered Exercises
	Chapter 7. LINEAR INDEPENDENCE
		7.1. Background
		7.2. Exercises
		7.3. Problems
		7.4. Answers to Odd-Numbered Exercises
	Chapter 8. BASIS FOR A VECTOR SPACE
		8.1. Background
		8.2. Exercises
		8.3. Problems
		8.4. Answers to Odd-Numbered Exercises
Part 3. LINEAR MAPS BETWEEN VECTOR SPACES
	Chapter 9. LINEARITY
		9.1. Background
		9.2. Exercises
		9.3. Problems
		9.4. Answers to Odd-Numbered Exercises
	Chapter 10. LINEAR MAPS BETWEEN EUCLIDEAN SPACES
		10.1. Background
		10.2. Exercises
		10.3. Problems
		10.4. Answers to Odd-Numbered Exercises
	Chapter 11. PROJECTION OPERATORS
		11.1. Background
		11.2. Exercises
		11.3. Problems
		11.4. Answers to Odd-Numbered Exercises
Part 4. SPECTRAL THEORY OF VECTOR SPACES
	Chapter 12. EIGENVALUES AND EIGENVECTORS
		12.1. Background
		12.2. Exercises
		12.3. Problems
		12.4. Answers to Odd-Numbered Exercises
	Chapter 13. DIAGONALIZATION OF MATRICES
		13.1. Background
		13.2. Exercises
		13.3. Problems
		13.4. Answers to Odd-Numbered Exercises
	Chapter 14. SPECTRAL THEOREM FOR VECTOR SPACES
		14.1. Background
		14.2. Exercises
		14.3. Answers to Odd-Numbered Exercises
	Chapter 15. SOME APPLICATIONS OF THE SPECTRAL THEOREM
		15.1. Background
		15.2. Exercises
		15.3. Problems
		15.4. Answers to Odd-Numbered Exercises
	Chapter 16. EVERY OPERATOR IS DIAGONALIZABLE PLUS NILPOTENT
		16.1. Background
		16.2. Exercises
		16.3. Problems
		16.4. Answers to Odd-Numbered Exercises
Part 5. THE GEOMETRY OF INNER PRODUCT SPACES
	Chapter 17. COMPLEX ARITHMETIC
		17.1. Background
		17.2. Exercises
		17.3. Problems
		17.4. Answers to Odd-Numbered Exercises
	Chapter 18. REAL AND COMPLEX INNER PRODUCT SPACES
		18.1. Background
		18.2. Exercises
		18.3. Problems
		18.4. Answers to Odd-Numbered Exercises
	Chapter 19. ORTHONORMAL SETS OF VECTORS
		19.1. Background
		19.2. Exercises
		19.3. Problems
		19.4. Answers to Odd-Numbered Exercises
	Chapter 20. QUADRATIC FORMS
		20.1. Background
		20.2. Exercises
		20.3. Problems
		20.4. Answers to Odd-Numbered Exercises
	Chapter 21. OPTIMIZATION
		21.1. Background
		21.2. Exercises
		21.3. Problems
		21.4. Answers to Odd-Numbered Exercises
Part 6. ADJOINT OPERATORS
	Chapter 22. ADJOINTS AND TRANSPOSES
		22.1. Background
		22.2. Exercises
		22.3. Problems
		22.4. Answers to Odd-Numbered Exercises
	Chapter 23. THE FOUR FUNDAMENTAL SUBSPACES
		23.1. Background
		23.2. Exercises
		23.3. Problems
		23.4. Answers to Odd-Numbered Exercises
	Chapter 24. ORTHOGONAL PROJECTIONS
		24.1. Background
		24.2. Exercises
		24.3. Problems
		24.4. Answers to Odd-Numbered Exercises
	Chapter 25. LEAST SQUARES APPROXIMATION
		25.1. Background
		25.2. Exercises
		25.3. Problems
		25.4. Answers to Odd-Numbered Exercises
Part 7. SPECTRAL THEORY OF INNER PRODUCT SPACES
	Chapter 26. SPECTRAL THEOREM FOR REAL INNER PRODUCT SPACES
		26.1. Background
		26.2. Exercises
		26.3. Problem
		26.4. Answers to the Odd-Numbered Exercise
	Chapter 27. SPECTRAL THEOREM FOR COMPLEX INNER PRODUCT SPACES
		27.1. Background
		27.2. Exercises
		27.3. Problems
		27.4. Answers to Odd-Numbered Exercises
	Bibliography
	Index