The Department of MATHEMATICS & STATISTICS Concordia University

 MAST 252 Linear Algebra II Winter 2004

Instructor:Dr. Ming Mei

Office/Tel No.:LB 541-1 / 848-2424 ext. 3236

Email:mei@mathstat.concordia.ca

Course Website:http://www.math.mcgill.ca/~mei/teaching.html

Office Hours:Thursday 14:00-15:00

Course Examiner:  Dr. A. Sierpinska

Texts:
A Schaum's Outlines, Linear Algebra, Third Edition, S.Lipschutz, McGraw-Hill.
B Schaum's Solved Problems Series, 3000 solved problems in Linear Algebra, S. Lipschutz, McGraw-Hill.

Assignments: You will not be required to hand in assignments. However, you will find below a list of valuable problems that correspond to the topics of the different weeks.

Test: There will be one class test in the seventh week of the course , covering the first five weeks of the course. There will be no make-up test.

Final Exam: The final examination will be three hours long. It covers material from the entire course, but there may be more stress on material covered in the second half of the course.

Final Mark: Your final mark will be computed as follows:

Test: 30% plus Final Exam: 70% = 100%
 Week Section (Book A) Topics Problems 1 7.2, 7.3 Inner products and examples. A: 7.2, 7.4, 7.5 B: 14.2, 14.4, 14.18, 14.19, 14.23, 14.24, 14.37 2 7.4, 7.5 Cauchy-Schwarz Inequality, orthogonality, orthogonal complements. A: 7.6, 7.7, 7.8, 7.9, 7.10, 7.11, 7.12, 7.13,  B: 14.81, 14.82, 14.96, 14.118, 14.119, 14.121 3 7.6, 7.7 Orthogonal bases, Gram-Schmidt orthogonalization. A: 7.14, 7.15, 7.16, 7.21, 7.22 B: 14.149, 14.153 4 7.8 Orthogonal matrices. A: 7.32, 7.33, 7.35, 7.36, 7.37, 7.38 B: 14.156, 14.165 5 9.2, 9.3 Polynomials of matrices, characteristic polynomial, Cayley Hamilton theorem. A: 9.7, 9.8 B: 15.29, 15.30, 15.32, 15.34, 15.41, 15.42, 15.45, 15.46, 15.47 6 9.7, 9.8 Minimal polynomial, characteristic and minimal polynomials of block matrices. Theorems 9.15, 9.16 A: 9.33, 9.34 B: 16.13, 16.14, 16.16, 16.18, 16.21 7 Test 8 10.3, 10.4 Invariance. Invariant direct-sum decompositions. A: 10.1, 10.2, 10.3, 10.4, 10.5,10.6,10.8, 10.10 B: 17.6, 17.17 9 10.5 Primary decomposition. A: 10.11, 10.12 B: 17.26, 17.46 10 10.6 Nilpotent operators. A: 10.17, 10.47, 10.48, 10.49, 10.51 B: 17.48-17.52, 17.56, 17.63 11 10.7 Jordan  Canonical Form. A: 10.13, 10.16, 10.17, 10.19, 10.20 B: 17.78, 17.79, 17.80, 17.81, 17.84, 17.85, 17.86, 17.87, 17.88, 17.89, 17.90, 17.97 12 10.8, 10.9 Cyclic subspaces, rational canonical form. A: 10.29, 10.32, 10.57, 10.60, 10.61, 10.62, 10.64 B: 17.140, 17.141, 17.142, 17.143, 17.144, 17.146, 17.147, 17.148, 17.149, 17.155, 17.159, 17.160 13 Review