Simultaneous Unitary Similarity and Congruence

When
Start: 10/23/2013 - 4:15pm
End  : 10/23/2013 - 5:15pm

Category
Colloquium

Speaker
Roger A. Horn, University of Utah

Abstract

Square complex matrices $ A $ and $ B $ are unitarily similar if there is a
unitary matrix $ U $ such that $ A=UBU^{\ast} $ (conjugate transpose); they are
unitarily congruent if there is a unitary $ U $ such that $ A=UBU^{T} $.

It is not difficult to determine whether a given pair of matrices is unitarily
similar. In fact, one can do so with finitely many ordinary arithmetic
operations.

However, the situation seems to be quite different for unitary congruence. The
best known result says that two given matrices are unitarily congruent if and
only if three specific pairs of matrices are simultaneously unitarily similar
(that is, the same $ U $ works for all three pairs).

So...how can we determine whether finitely many pairs of matrices are
simultaneously unitarily similar? What about simultaneous unitary congruence
of finitely many pairs of matrices?

Where
Davidson Lecture Hall, Claremont McKenna College

AttachmentSize
Horn.pdf127.58 KB