MATH 7822 Topics in Linear Algebra
Spring 2009
Department of Mathematical Sciences
University of Colorado Denver

HOURS, PLACE: TR 4-5:15 pm, CU (Dravo) 626.

INSTRUCTOR:
Prof. Andrew Knyazev
Office: CU (Dravo) 644. Phone: 556-8102.
Office hours: by appointment
WWW: http://www-math.ucdenver.edu/~aknyazev/

TEXTBOOKS: Required:

Matrix Analysis by Roger A. Horn, Charles R. Johnson ISBN-10: 0521386322 ISBN-13: 978-0521386326 Cambridge University Press; 1990.

Suggested independent reading

Finite-Dimensional Linear Analysis by I. M. Glazman, Ju. I. Ljubic, G. Kuerti (Editor), G. P. Barker (Translator) Dover Publications, 2006, ISBN-10: 0486453324, ISBN-13: 978-0486453323

Optional independent reading

Inequalities: Theory of Majorization and Its Applications by Albert W. Marshall, Ingram Olkin, Barry Arnold ISBN:  0387400877, 978-0387400877  Publisher  Springer; 2nd edition (not yet published)

SUBJECT:

CONTENTS:
The class will mostly follow the outline below, touching on each major topic in a depth that will be determined by the pace of the class:

• Review and miscellanea
• 1. Eigenvalues, eigenvectors, and similarity
• 2. Unitary equivalence and normal matrices
• 3. Canonical forms (independent reading)
• 4. Hermitian and symmetric matrices
• 5. Norms for vectors and matrices
• 6. Location and perturbation of eigenvalues
• 7. Positive definite matrices
• 8. Non-negative matrices

GRADING will be based on research projects:

• Stability of the Jordan form