MAT 224H - LINEAR ALGEBRA II
COURSE OUTLINE
Summer, 2004

Section L0101 L5101

Instructors Kyu-Hwan Lee Marcos Escobar-Anel

Office SS5016E SP205

Office Hours Thur. 10-12 Mon. 5-6

Tel. 978-4328 946-5808

Time Thur. 1-4 Thur. 6-9

Location LM 161 RW 143

Textbook
W.K. Nicholson: Linear Algebra with Applications , 4th edition.

Grading Scheme
Your final grade will be determined as follows:
1st Midterm --- 25%,   2nd Midterm --- 25%,   Final --- 50%.

Midterm test
There will be two 75 minutes midterm tests. The first one will be on June 24, and the second on July 29. There will be no make up tests.

Tutorials

Section L0101 (Last Name A-N) L0101 (Last Name O-Z) L5101

TA's Adam Gregson Allan Langridge Lindsey Shorser

Time Thur. 4-5 Thur. 4-5 Thur. 5-6

Location LM 123 LM 155 RW 143

During your tutorials the T.A. will discuss with you some problems from the list below. Feel free to ask questions about the problems you have difficulty with.

Remarking Procedure
Your tests will be returned to you in the tutorial section in which you are registered as soon as they are marked. If you have any questions about the marking of your test, you will have to return your test to your T.A. within 10 min indicating on the front page which question you want to be remarked. If you take your paper with you, no one will look at it again. No test will be remarked unless the original answers were written in ink.

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Brief Description
This is the second course in Linear Algebra, that is more theoretical in nature then your first course (Linear Algebra I - MAT223). The course will cover: abstract vector spaces, linear mappings, linear operators on both real and complex vector spaces, inner product spaces, orthogonal (unitary) diagonalization of linear operators, isometries. It will be assumed that you know basic material from Linear Algebra I, particularly: matrix arithmetic, similarity and diagonalization of matrices and the basic concepts of the n-space R^n including orthogonality.

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Schedule and Suggested Problems
You should solve, at the very minimum, the problems on the list below.

WEEK 1: Complex n-space C^n and its inner product, Complex Matrices, Spectral Theorem
App. A #3(b), 3(f), 4(d), 5(b), 9, 11(d), 14
7.6 # 1(d), 2(d), 3, 4(b), 4(d), 5(b), 5(d), 5(f), 6(b), 6(f), 7, 8, 9, 11, 12, 13, 15, 18, 19, 22

WEEK 2: Orthogonal diagonalization, Quadratic forms, positive definite forms
7.2 # 1(f), 2, 4, 5(d), 5(f), 6, 7, 10, 11, 12, 14, 15, 17, 18, 23
7.7 # 1(d), 2(b), 2(d), 2(f)/Q2- diagonalization only/, 3(b), 3(d), 9(a)
7.3 # 2, 3, 4, 5, 7, 9, 10

WEEK 3: Vector Spaces and Subspaces
6.1 # 1, 2, 3, 4, 6, 8, 10, 11, 12, 15, 16
6.2 # 1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 13, 14, 15, 16,  20, 27

WEEK 4: The Dimension Theory
6.3 # 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 13, 14, 15, 16, 17, 19, 21, 23, 24, 28, 30, 32, 35
6.4 # 1, 2, 3, 4, 5, 6,7, 8, 9, 11, 12, 13, 17, 19(a), 22

WEEK 5: Linear Transformations
8.1 # 1, 2, 3, 4, 5, 11, 12, 13, 14, 15, 16, 17, 18, 19, 21
8.2 # 1(b), 1(d),  2, 4, 5, 6, 7, 8, 10, 11, 12, 13, 14, 15, 17, 20

WEEK 6: 1st Midterm (It covers Ch. 6 &7.), Isomorphism
8.3 # 1, 2, 4, 5, 6, 7, 9, 10, 12, 13, 14, 15, 23, 26

WEEK 7: No lecture (Canada Day)

WEEK 8: Matrix Representation of Linear Transformations
8.4 #1, 2, 3, 4, 5(d), 6, 7(d), 8, 9, 12, 16(a), 17, 18(a), 19, 22

WEEK 9: Change of Basis, Invariant Subspaces
8.5 # 1, 2, 3, 4(b), 5(a), 6, 7, 8(a), 9(d), 9(f), 10, 11, 14
8.6 # 1, 2, 3, 4, 5, 6, 8, 9

WEEK 10: Direct Sums, Cayley-Hamilton Theorem, Jordan Canonical Form
8.6 # 10(b), 10(c), 10(d), 11, 12, 13, 14, 15, 17, 18, 19, 20, 22, 23, 24, 25(a), 25(b)
8.7 # 1, 2, 3, 4, 5, 6, 7

WEEK 11: 2nd Midterm (It covers Ch. 8.), Inner Product Spaces
9.1 # 1, 3, 4, 5, 6, 7, 9, 10, 12, 13, 14, 16, 18, 23, 25, 26, 27, 28, 30, 32

WEEK 12: Orthogonal diagonalization
9.2 # 1, 2(b), 3(b), 4, 5, 6(c)-(f), 7, 8, 9, 10, 11, 13, 14, 15
9.3 # 1, 2, 3, 4, 5(b), 5(d), 6, 8, 12, 13, 15

WEEK 13: Isometries, Unitary Spaces
9.4 # 1(c), 2(d), 2(f), 3(b), 3(d), 3(f), 6, 8, 10