Reducing the Size of a Matrix While Maintaining its Spectrum

SIAM Student Seminar
Friday, January 22, 2010 - 1:00pm for 1 hour (actually 50 minutes)
Skiles 255
Benjamin Webb – School of Mathematics, Georgia Tech
Linwei Xin
The Fundamental Theorem of Algebra implies that a complex valued nxn matrix has n eigenvalues (including multiplicities). In this talk we introduce a general method for reducing the size of a square matrix while preserving this spectrum. This can then be used to improve on the classic eigenvalue estimates of Gershgorin, Brauer, and Brualdi. As this process has a natural graph theoretic interpretation this talk should be accessible to most anyone with a basic understanding of matrices and graphs. These results are based on joint work with Dr. Bunimovich.