Math 2371: MATRICES & LINEAR OPERATORS II Spring 2009
Instructor: David
Swigon
Office: Thackeray 511, 4126244689, swigon@pitt.edu
Lectures:
MWF 11:0011:50am, Thackeray 704
Recitations: Th 1010:50am, Thackeray
704, Instructor Jonathan Holland
jonathan.e.holland@gmail.com
Office
Hours: MWF 3pm4pm, Thackeray 511, or
by appointment.
Course
Web Page: (check frequently for changes and updates) http://www.math.pitt.edu/~swigon/math2371.html
Prerequisites
Math 2370
or equivalent.
Textbook
(Available
at The Book Center on Fifth Ave.)
A higher
level mathematical monograph chosen for its axiomatic approach to the subject
and its contents, which include most of the topics to be covered in the course.
Other recommended books
Beautifully
written book that provides brief and tothepoint explanation of the main
concepts and their motivations. Should be read alongside of Lax.
Book
written from the point of view of abstract algebra. Rich in examples and
exercises, covers more than necessary.
Undergraduate
level, focuses on matrices, good for first reading or as a refresher.
Grading
Scheme
Quizzes: 10%
Homework: 25%
Midterm
Exam: 30%
Final
Exam: 35%
The final
exam for this course is a part of the Mathematics Department Preliminary Exam
in Linear Algebra
Schedule
Tentative
syllabus is given below, with a list of assigned reading for the week.
Every Friday
a list of practice problems for the next week will be given. The students are
expected to work out the practice problems and consult the instructor if
difficulties arise. Few times during the term, with advance notice, the
problems will be collected and graded as a homework. The approximate schedule
and a list of practice problems will be posted below.
Every
Friday the lecture will start with a 20 min quiz based on the material covered
since the last quiz. Quizzes will be graded and will count towards the final
grade.
The
recitations on Thursdays will be spend on the discussion of practice problems
assigned for the week, so please come prepared.
Syllabus
Week 
Reading 
Topics 
Practice
problems 
Notes 
Jan
5 – Jan 9 
[L]
8 
Review:
Normal maps, Rayleigh quotient, minmax principle 


Jan
12 – Jan 16 
[L]
9 
Calculus
of matrix and vector valued functions; Matrix exponential 

M.L.
King holiday Jan
21 – Jan 23 
[L]
9 
Simple
and multiple eigenvalues 
Set III is a homework due 

Jan
26 – Jan 30 
[L]
9 
Simple
and multiple eigenvalues 

Feb
2  Feb 6 
[L]
10 
Matrix
inequalities; positive definite matrices 

Feb
9  Feb 13 
[L]
10 
Eigenvalues
of positive matrices 


Feb
16 – Feb 20 
[L]
10 
Representations
of mappings 

Feb
23 – Feb 25 

Review 


Feb
27 

Midterm Exam Covers
[L] 810 + Polar and Singular value decomposition 


Mar
2 – Mar 6 
[L]
12 
Convexity;
HahnBanach theorem 
Set VI is a homework due 

Mar 9 – Mar 13 

Spring Break 


Mar
16 – Mar 20 
[L]
12 
Caratheodory theorem 

Mar
23 – Mar 27 
[L]
14 
Normed
linear spaces 

Mar
30 – Apr 3 
[L]
A 
Gershgorin
circle theorem; 

Apr
6 – Apr 10 
[L]
13 
Minmax
theorem 

Apr
13 – Apr 17 
[L]
16 
Positive
matrices, Perron theorem 


Apr
20 

Review 


Friday Apr 24 

Linear Algebra Prelim Exam 11am – 2pm 
