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CATEGORIES:Lectures & Workshops
DESCRIPTION:Speaker: Greg Friedman\, Texas Christian University\n\nTitle: T
opological linear algebra - the unitary equivalence of matrices over topolo
gical spaces\n\n(joint with Efton Park\, Texas Christian University)\n\nAbs
tract: As an application of topology to linear algebra\, we study the quest
ion of unitary equivalence for matrices with coefficients in the ring C(X)
of continuous complex-valued functions over a topological space X (equivale
ntly\, one can imagine a family of matrices that varies continuously over t
he 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 si
ngle cohomological obstruction that completely determines whether A and B a
re unitary equivalent. Using this tool\, it is often possible to count or b
ound the number of unitary equivalence classes on X with given eigenvalues.
This generalizes work of Grove and Pedersen on the diagonalizability of no
rmal matrices with coefficients in C(X).
DTEND:20230508T190000Z
DTSTAMP:20231206T212245Z
DTSTART:20230508T180000Z
GEO:32.986102;-96.751378
LOCATION:Engineering and Computer Science West (ECSW)\, 1.315
SEQUENCE:0
SUMMARY:GTDS Seminar: Greg Friedman
UID:tag:localist.com\,2008:EventInstance_42540431556888
URL:https://calendar.utdallas.edu/event/gtds_seminar_greg_friedman
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