Monday, May 8 at 1:00pm to 2:00pm
Engineering and Computer Science West (ECSW), 1.315
800 W. Campbell Road, Richardson, Texas 75080-3021
Speaker: Greg Friedman, Texas Christian University
Title: Topological linear algebra - the unitary equivalence of matrices over topological spaces
(joint with Efton Park, Texas Christian University)
Abstract: As an application of topology to linear algebra, we study the question of unitary equivalence for matrices with coefficients in the ring C(X) of continuous complex-valued functions over a topological space X (equivalently, one can imagine a family of matrices that varies continuously over the points of X). If X is a CW complex and A and B are normal matrices over C(X) with the same set of distinct eigenvalues, we show that there is a single cohomological obstruction that completely determines whether A and B are unitary equivalent. Using this tool, it is often possible to count or bound the number of unitary equivalence classes on X with given eigenvalues. This generalizes work of Grove and Pedersen on the diagonalizability of normal matrices with coefficients in C(X).
UTD strives to create inclusive and accessible events in accordance with the Americans with Disabilities Act (ADA). If you require an accommodation to fully participate in this event, please contact the event coordinator (listed below) at least 10 business days prior to the event. If you have any additional questions, please email ADACoordinator@utdallas.edu and the AccessAbility Resource Center at firstname.lastname@example.org.