The contents will be adjusted as the course progresses.
- Jan 21. §1.1 Vectors and Linear Combinations
- Jan 23. §1.2 Lengths and Dot Products
- Jan 26. §1.3 Matrices
- Jan 28. §2.1 Vectors and Linear Equations
- Jan 30. §2.2 Elimination
- Feb 2. §2.4 Matrix Operations
- Feb 4. §2.3 Elimination Using Matrices
- Feb 6. §2.5 Inverse Matrices
- Feb 9. §2.5 Gauss-Jordan Elimination
- Feb 11. §2.6 Elimination = Factorization: A = LU
- Feb 13. §2.6 A=LDU and §2.7 Transposes
- Feb 16. No class (February break)
- Feb 18. §3.1 Spaces of Vectors
- Feb 20. §3.1 Column Space and §3.2 Nullspace
- Feb 23. §3.2 Nullspace
- Feb 25. Review
- Feb 25, 7:30-9:00. Prelim 1
- Feb 27. §3.3 Rank and Row Reduced Form
- Mar 2. §3.4 The Complete Solution to Ax = b
- Mar 4. §3.6 Row Space and §3.5 Independence
- Mar 6. §3.5 Independence and Basis
- Mar 9. §3.5 Basis and §3.6 Left Nullspace
- Mar 11. §8.2 Graphs and Incidence Matrices
- Mar 13. §8.2 Incidence Matrices. Polyhedra and Euler's Formula
- Mar 16. §4.1 Orthogonality
- Mar 18. §4.1 Orthogonality of the Four Subspaces. Incidence matrices
- Mar 20. §4.3 Least Squares Approximations
- Mar 23. §4.3 Least Squares Approximations and §4.2 Projections (onto lines)
- Mar 25. §4.4 Gram-Schmidt. Orthogonal matrices
- Mar 27. §4.4 QR factorization and §4.3 Gauss and Ceres
- Mar 30-Apr 3. Spring break
- Apr 6. No class--illness
- Apr 8. §5.2 Determinants. Definition. Cofactors, row and column expansion
- Apr 10. §5.1 Determinant of the transpose. Multilinear and alternating. Determinant of a product. Area and volume
- Apr 13. §5.3 Row operations. Non-zero determinant. Cofactors and inverses
- Apr 15. §6.1 Eigenvalues and Eigenvectors
- Apr 17. Eigenvector centrality
- Apr 20. §6.2 Diagonalization
- Apr 22. Review
- April 23, 7:30-9:00. Prelim 2
- Apr 24. §6.2 Diagonalization and powers of matrices
- Apr 27. No class (Cornell's anniversary)
- Apr 29. §6.2 Diagonalization and linear recursions
- May 1. §8.3 Transition matrices (Markov processes)
- May 4. §8.3 Perron-Frobenius Theorem
- May 6. Google's PageRank
- May 13, 2:00-4:30. Final Exam
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