# Courses

## 01:640:350:H - Linear Algebra Honors Section

### Prof. Weibel (640:350:H1) — Fall 2017

This course is a proof-based continuation of Math 250, covering Abstract vector spaces and linear transformations, inner product spaces, diagonalization, and canonical forms.

Prerequisites:

CALC4, Math 250 and Math 300

Text: Linear Algebra (4th ed.), by Friedberg, Insel and Spence,
Prentice Hall, 2003   ISBN 0-13-008451-4.

• Lectures MW6 (5:00-6:20PM) in ARC 333
• Weibel's Office hours: Monday 1:30-2:45 PM; Wednesday 10:30AM-12 noon

#### Tentative Course Syllabus

WeekLecture dates Sections   topics
1 9/6 (W)  Chapter 1 Abstract vector spaces & subspaces
2 9/11 (M), 13 (W) Chapter 1 Span of subsets, linear independence
3 9/18, 20 Chapter 1 Bases and dimension
4 9/25, 27 Chapter 2 Linear transformations
5 10/2, 10/4 Chapter 2 Change of basis, dual spaces
6 10/9, 10/11 Ch. 1-2  Review and Exam 1
7 10/16, 10/18 Chapter 3  Rank and Systems of Linear Equations
8 10/23, 10/25 Chapter 4  Determinants and their properties
9 10/30, 11/1 Chapter 5  Eigenvalues/eigenvectors
10 11/6, 11/8 Chapter 5  Cayley-Hamilton
11 11/13, 11/15 Chapter 7  Jordan Canonical Form
12 11/20 Chapter 7  Rational Canonical Form
13 11/27, 11/29  Ch.3,4,5,7  Review and Exam 2
14 12/4, 12/6 Chapter 6  Inner Product spaces
15 12/11, 12/13 Chapter 6  Unitary and Orthogonal operators (last class)
17 December 21 (Thursday) 4-7 PM Final Exam

#### Homework Assignments

td>6.3 #17,22(c); 6.5 #6,7

HW Due on:HW Problems (due Wednesdays)
Sept. 13 1.2 #17; 1.3 #19,23; 1.4 #11,13; 1.5 #9,15
Sept. 20 1.6 #20,26,29; 1.7 #5,6; 2.1 #3,11,28 Show that P(X) is a vector space
over F2, and find a basis
Sept. 27 2.2 #6; 2.3 #12; 2.4 #15,21; 2.5 #3(d),8,13
Oct. 4 2.6#10; 2.7#11,14; 3.1#6,12; 3.2#9; 3.3#10 Show that F[t]* is iso. to F[[x]]
Oct. 25 4.1 #11; 4.2 #24, 29; 4.3 #10,12,21
Nov. 1 5.1 #3b, 20, 33a; 5.2 #4, 9a, 12
Nov. 8 5.3 #6; 5.4 #13,17,21,27,36
Nov. 15 7.1 #3b,9b,11; 7.2 #3,14,19a;
7.3 #13,14
Find all 4x4 Jordan canonical forms satisfying T2=T3
Dec. 13 6.1 #11,27(b,c),28; 6.2 #6,10; 6.3 #17,22(c); 6.5 #6,7

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