M. Mathieu

will speak on

A multivariable Cayley--Hamilton theorem

Time: 4:00PM
Date: Tue 4th September 2007
Location: ENG226 [map]

Further information

Abstract: The Weyl calculus for a pair A = (A1,A2) of selfadjoint n × n matrices,
due to H. Weyl, associates a matrix WA(f) to each smooth function f defined on $R^2$ in a linear but typically not multiplicative way. Letting cA(λ) =
det((A1 - λ1)2 + (A2 - λ2)2) for λ = (λ1
,λ2) $\in\mathbb{R}^2$ denote the joint characteristic polynomial of the pair A it is known, for n ≤ 3, that A
1A2 = A2A1 if and
only if WA(cA) = 0. It is an open problem whether this is still true for n > 3. We shall discuss two new approaches to this problem: the role of the
canonical order structure for selfadjoint matrices; and topological invariants
arising from
continuity properties of the non-linear map (f,A) ↦→ W
A(f). This is joint work
with W. Ricker, Eichstatt, Germany to be published in Math. Proc
. Royal Ir. Acad.

(This talk is part of the IMS September Meeting 2007 series.)

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