Linear Algebra¶
Textbook Information¶
Stephen H. Friedberg, Arnold J. Insel, Lawrence E. Spence - Linear Algebra, 4th Edition
Table of Contents¶
Ch 1. Vector Spaces¶
- [1. Introduction]
- 2. Vector Spaces
- 3. Subspaces
- 4. Linear Combinations and Systems of Linear Equations
- 5. Linear Dependence and Linear Independence
- 6. Bases and Dimension
- 7. Maximal Linearly Independent Subsets
Ch 2. Linear Transformations and Matrices¶
- 8. Linear Transformations, Null Spaces, and Ranges
- 9. The Matrix Representation of a Linear Transformation
- 10. Composition of Linear Transformations and Matrix Multiplication
- 11. Invertibility and Isomorphisms
- 12. The Change of Coordinate Matrix
- [13. Dual Spaces]
- [14. Homogeneous Linear Differential Equations with Constant Coefficients]
Ch 3. Elementary Matrix Operations and Systems of Linear Equations¶
- 15. Elementary Matrix Operations and Elementary Matrices
- 16. The Rank of a Matrix and Matrix Inverses
- 17. Systems of Linear Equations - Theoretical Aspects
- 18. Systems of Linear Equations - Computational Aspects
Ch 4. Determinants¶
- 19. Determinants of Order 2
- 20. Determinants of Order n
- 21. Properties of Determinants
- [22. A Characterization of the Determinant]
Ch 5. Diagonalization¶
- 23. Eigenvalues and Eigenvectors
- 24. Diagonalizability
- [25. Matrix Limits and Markov Chains]
- 26. Invariant Subspaces and the Cayley-Hamilton Theorem
Ch 6. Inner Product Spaces¶
- 27. Inner Products and Norms
- 28. The Gram-Schmidt Orthogonalization Process and Orthogonal Complements
- 29. The Adjoint of a Linear Operator
- 30. Normal and Self-Adjoint Operators
- 31. Unitary and Orthogonal Operators and Their Matrices
- 32. Orthogonal Projections and the Spectral Theorem
- 33. The Singular Value Decomposition and the Pseudoinverse
- [34. Bilinear and Quadratic Forms]
- [35. Einstein's Special Theory of Relativity]
- [36. Conditioning and the Rayleigh Quotient]
- [37. The Geometry of Orthogonal Operators]
Ch 7. Canonical Forms¶
- [38. The Jordan Canonical Form I]
- [39. The Jordan Canonical Form II]
- [40. The Minimal Polynomial]
- [41. The Rational Canonical Form]