Tue, 23 Feb 2010
17:00 -
18:37
L3
Monotone Matrix functions in several variables
John McCarthy
(Washington Univ St Louis and Trinity College Dublin)
Abstract
In 1934, K. Loewner characterized functions that preserve
matrix inequalities,
i.e.\ those f with the property that whenever A and B are self-adjoint
matrices of the same dimension,
with $A \leq B$, then $f(A) \leq f(B)$.
In this talk, I shall discuss how to characterize monotone matrix
functions of several variables,
namely functions f with the property that if $A = (A_1, \dots , A_n) $
is an n-tuple of commuting self-adjoint matrices,
and $B = (B_1, \dots, B_n)$ is another, with each $A_i \leq B_i$, then
$f(A) \leq f(B)$.