Linear Algebra II Winter 2004 
Instructor:Dr. Ming Mei
Office/Tel No.:LB 5411 / 8482424 ext. 3236
Email:mei@mathstat.concordia.ca
Course Website:http://www.math.mcgill.ca/~mei/teaching.html
Office Hours:Thursday 14:0015:00
Course Examiner: Dr. A. Sierpinska
Texts:
A Schaum's Outlines, Linear Algebra,
Third Edition, S.Lipschutz, McGrawHill.
B Schaum's Solved Problems Series,
3000 solved problems in Linear Algebra, S. Lipschutz, McGrawHill.
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 makeup 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  CauchySchwarz 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, GramSchmidt 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 directsum 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: 17.4817.52, 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 


