Mathematics 3107 Linear Algebra III

 
Course Outline
 
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. 15-19: reading week.
  • 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.
    •  

    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.