matrix monotone

A real function f on a real interval I is said to be matrix monotone of n, if

ALBf(A)f(B) (1)

for all Hermitian n×n matrices A,B with spectra contained in I. Here L denotes the Loewner order, and the notation f(A) is explained in the entry functional calculus for Hermitian matrices.

Title matrix monotone
Canonical name MatrixMonotone
Date of creation 2013-03-22 13:34:57
Last modified on 2013-03-22 13:34:57
Owner mathcam (2727)
Last modified by mathcam (2727)
Numerical id 12
Author mathcam (2727)
Entry type Definition
Classification msc 40A30
Related topic ALeqBForHermitianMatricesAB
Related topic OperatorMonotone