Lectures and Homework 642:550, Summer 2009

Homework is due two class meetings following the assignment date, allowing for questions about the assignment to be  discussed in one class meeting between assignment and collection. References are to the hardbound version of the fourth edition of the textbook. Other versions of the textbook (including the "International Edition" of the fourth edition) may have different problems. Review problems athe the end of a chapter are indicated by R and problems from my supplements (available from this site) are indicated by S.

1. June 22: Prerequisites
   • 2.4: 18, 20.
   • 2R: 11.
   • 3.1: 16, 38.
   • S1: A, B.
2. June 23: Determinants
   • 4.2: 4, 18, 34.
   • 4.3: 1&2, 8.
3. June 25: Applications of Determinants; Introduction to eigenvalues.
   • 4.4: 2, 18a, 20, 28. (In 28, note that faces are 2 dimensional, so area needs something different than the formula for volume.)
   • 4R: 15.
   • S3: A, B, C.
   • 4.3: 1&2&3, 14.
4. June 29: Finding eigenvalues and eigenvectors.
   • 5.2: 2, 4, 8, 24.
   • S4: A, C, E, G.
   • 5.3: 14, 24.
5. June 30: Complex matrices.
   • 5.5: 6, 7&8, 26, 49.
   • 5R: 15.
6. July 02: Matrix Exponentials.
   • S5: A, D, E, H, V, X.
7. July 06: The QR factorization; Schur's triangulariation theorem.
   • 3.4: 2, 14, 28, 32.
   • S6: A, B, C, D.
8. July 07: Least squares; Singular Value Decomposition.
   • 3.3: 6, 18, 22. Note that part b of exercise 18 asks for a least squares solution.
   • 6.3: 1&2, 18. Note that part c of exercise 2 asks to relate the SVD in part b to the four fundamental subspaces of A.
   • S7: NONE.
9. July 09: Positive definite quadratic forms.
   • 6.1: 2, 14.
   • 6.2: 2, 6, 14, 28.
10. July 13: Minimum principles.
    • 6.4: 6, 16. In addition, solve the following modifications of problem 6: (A) change the diagonal to 3, 1; (B) change the off diagonal terms to 2; (C) make both changes.
11. July 14: The Perron-Frobenius theorem.
    • S8: A, B, C, D.
12. July 16: Finding characteristic polynomials.
    • S9: A, B, C.
13. July 20: Matrix norms, computing eigenvectors.
    • 7.2: 4, 18.
    • S10: A, B.
    • 7.3: NONE.
14. July 21: Iterative methods for linear systems.
    • 7.4: NONE.