Math 2371: MATRICES & LINEAR OPERATORS II Spring 2009

Instructor: David Swigon

Office: Thackeray 511, 412-624-4689, swigon@pitt.edu

Lectures:  MWF 11:00-11:50am, Thackeray 704

Recitations: Th 10-10:50am, Thackeray 704, Instructor Jonathan Holland jonathan.e.holland@gmail.com

Office Hours: MWF 3pm-4pm, 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 to-the-point 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

Set I

 

Jan 12 Jan 16

[L] 9

Calculus of matrix and vector valued functions; Matrix exponential

Set II

Quiz 1 solution

M.L. King holiday

Jan 21 Jan 23

[L] 9

Simple and multiple eigenvalues

Set III is a homework due
Fri, Jan 23

Quiz 2 solution

Jan 26 Jan 30

[L] 9

Simple and multiple eigenvalues

Quiz 3 solution

Feb 2 - Feb 6

[L] 10

Matrix inequalities; positive definite matrices

Set IV

Quiz 4 solution

Feb 9 - Feb 13

[L] 10

Eigenvalues of positive matrices

Set V

 

Feb 16 Feb 20

[L] 10

Representations of mappings

Feb 23 Feb 25

 

Review

Practice Midterm

Solutions

 

Feb 27

 

Midterm Exam

Covers [L] 8-10 + Polar and Singular value decomposition

 

Mar 2 Mar 6

[L] 12

Convexity; Hahn-Banach theorem

Set VI is a homework due
Fri, Mar 20

 

Mar 9 Mar 13

 

Spring Break

 

 

Mar 16 Mar 20

[L] 12

Caratheodory theorem

Quiz 5 solution

Mar 23 Mar 27

[L] 14

Normed linear spaces

Set VII

Quiz 6 solution

Mar 30 Apr 3

[L] A

Gershgorin circle theorem;

Set VIII

Quiz 7 solution

Apr 6 Apr 10

[L] 13

Minmax theorem

Set IX

Apr 13 Apr 17

[L] 16

Positive matrices, Perron theorem

 

 

Apr 20

 

Review

Preliminary exam topics

Final Exam

 

 

Friday

Apr 24

 

Linear Algebra Prelim Exam

11am 2pm