## Mathematics 3107 Linear Algebra III

My office hours are: Thursday 2:30--3:30pm. HP4368. TA: to be announced. See CUlearn for solutions to midterms and assignments.

Topics covered in the class.

• Jan. 7: Introduction and complex numbers.
• Jan. 12: Polar forms and Euler's formula, Elementary matrices.
• Jan. 14: Elemenatary matrices, special matrices.
• Jan. 19: Invertible matrices, ranks, solve nonlinear systems.
• Jan. 21: LU (PLU) factatorization, tensor products.
• Jan. 26: Standard norm, inner product
• Jan. 28: Cross product, CBS inequality
• Feb. 2: Projection and angles.
• Feb. 4: Geometry of hyperplanes, Least square method.
• Feb. 9: Orthogonal and Unitary matrices.
• Feb. 11: Householder matrices, eigenvalues and eigenvectors.
• Feb. 23: More eigenvalues and eigenvectors, diagonalization.
• Feb. 25: Midterm
• Mar. 1: Diagonalization, discrete dynamical system
• Mar. 3: Discrete dynamical system, Markov chain, internet search engine.
• Mar. 8: Google search enginee, Jordan normal form.
• Mar. 10: Orthogonal diagonalization/unitarily diagonalization.
• Mar. 15: Schur Triangularization Theorem.
• Mar. 17: Applications of Schur Triangularization Theorem.
• Mar. 22: Singular Value Decomposition.
• Mar. 24: Singular Value Decomposition.
• Mar. 29: The Gershgorin Circle Theorem; power method.
• Mar. 31: Inverse power method; Norms.
• Apr. 5: Inner products, CBS inequalities;
• Apr. 7: Projections, Gram-Schmidt Process, QR factorization; Review.

 Tutorials Tutorial #1. Section 1.2: 9, 11, Section 2.4: 1, 5, 13, 15 Tutorial #2 Section 2.5: 5, 17 Section 2.6: 7, 13, 17 Section 2.7: 1, 3, 5. Tutorial #3. Section 4.1: 1 d), 3 b) d), 5 c), 11 Section 4.2: 3, 7, 11 Tutorial #4. Section 4.3: 3, 5, 7, 9, 11 Section 5.1: 1 (b)(e), 3 (b)(e). Tutorial #5. Section 5.1: 17, 19, 21. Section 5.2: 1 (b)(d), 3 (a)(d), 7. Tutorial #6. Section 5.2: 9, 11. Section 5.3: 1, 3. Tutorial #7. Section 5.3: 7, 9. Section 5.4: 1 (a) (d), 3(1) (b), 5. Tutorial #8. Section 5.4: 7, 12, 13. Section 5.5: 1, 5. Tutorial #9. Section 5.5: 1, 5, 7. Section 5.6: 1 (a) (b). Tutorial #10. Section 5.6: 4 (b). Section 5.7: 1 (a) (b) (c), 3.
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 Extra Suggested Exercises. Section 1.2: 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 24. Section 2.4: 1, 5, 7, 9, 11, 13, 15, 17, 19, 21, 25. Section 2.5: 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21. Section 2.6: 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21. Section 2.7: 1, 3, 5, 7, 9, 13. Section 4.1: 1, 3, 5, 7, 9, 11, 13, 15, 17. Section 4.2: 1, 3, 5, 7, 9, 11, 17. Section 4.3: 1, 3, 5, 7, 9, 11, 15, 17. Section 5.1: 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21. Section 5.2: 1, 3, 5, 7, 9, 11, 13, 15. Section 5.3: 1, 3, 5, 7, 9, 15, 17. Section 5.4: 1, 3, 5, 7, 9, 11, 13, 15, 17. Section 5.5: 1, 3. 5, 7, 9. Section 5.6: 1, 3, 5, 7. Section 5.7: 1, 3. Section 6.1: 1, 3, 5, 7.