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Proscribed normal decompositions of Euclidean Jordan algebras

Michael Orlitzky(michael***at***orlitzky.com)

Abstract: Normal decomposition systems unify many results from convex matrix analysis regarding functions that are invariant with respect to a group of transformations---particularly those matrix functions that are unitarily-invariant and the affiliated permutation-invariant "spectral functions" that depend only on eigenvalues. Spectral functions extend in a natural way to Euclidean Jordan algebras, and several authors have studied the problem of making a Euclidean Jordan algebra into a normal decomposition system. In particular it is known to be possible with respect to the "eigenvalues of" map when the algebra is essentially-simple. We show the converse, that essential-simplicity is essential to that process.

Keywords: Normal decomposition, spectral function, spectral set, Euclidean Jordan algebra,

Category 1: Convex and Nonsmooth Optimization (Convex Optimization )

Category 2: Global Optimization

Citation: June 30, 2020

Download: [PDF]

Entry Submitted: 06/30/2020
Entry Accepted: 06/30/2020
Entry Last Modified: 06/30/2020

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