Math 2371:MATRICES & LINEAR OPERATORS IISpring 2009
Office: Thackeray 511, 412-624-4689, email@example.com
Lectures: MWF 11:00-11:50am, Thackeray 704
Recitations:Th 10-10:50am, Thackeray 704, InstructorJonathan Holland firstname.lastname@example.org
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
Math 2370 or equivalent.
- Lax, Linear Algebra, Wiley-Interscience, 1996.ISBN: 0471111112
(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.
- Horn & Johnson, Matrix analysis
Other recommended books
- Halmos, Finite-Dimensional Vector Spaces
Beautifully written book that provides brief and to-the-point explanation of the main concepts and their motivations. Should be read alongside of Lax.
- Hoffman & Kunze, Linear Algebra
Book written from the point of view of abstract algebra. Rich in examples and exercises, covers more than necessary.
- Axler, Linear Algebra Done Right
Undergraduate level, focuses on matrices, good for first reading or as a refresher.
Midterm Exam: 30%
Final Exam: 35%
The final exam for this course is a part of the Mathematics Department Preliminary Exam in Linear Algebra
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.
Jan 5 – Jan 9
Review: Normal maps, Rayleigh quotient, minmax principle
Jan 12 – Jan 16
Calculus of matrix and vector valued functions; Matrix exponential
Quiz 1 solution
M.L. King holiday
Jan 21 – Jan 23
Simple and multiple eigenvalues
Set III is a homework due
Quiz 2 solution
Jan 26 – Jan 30
Simple and multiple eigenvalues
Quiz 3 solution
Feb 2 - Feb 6
Matrix inequalities; positive definite matrices
Quiz 4 solution
Feb 9 - Feb 13
Eigenvalues of positive matrices
Feb 16 – Feb 20
Representations of mappings
Feb 23 – Feb 25
Covers [L] 8-10 + Polar and Singular value decomposition
Mar 2 – Mar 6
Convexity; Hahn-Banach theorem
Set VI is a homework due
Mar 9 – Mar 13
Mar 16 – Mar 20
Quiz 5 solution
Mar 23 – Mar 27
Normed linear spaces
Quiz 6 solution
Mar 30 – Apr 3
Gershgorin circle theorem;
Quiz 7 solution
Apr 6 – Apr 10
Apr 13 – Apr 17
Positive matrices, Perron theorem
Preliminary exam topics
Linear Algebra Prelim Exam
11am – 2pm
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