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Rank computation in Euclidean Jordan algebras

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

Abstract: Euclidean Jordan algebras are the abstract foundation for symmetriccone optimization. Every element in a Euclidean Jordan algebra has a complete spectral decomposition analogous to the spectral decomposition of a real symmetric matrix into rank-one projections. The spectral decomposition in a Euclidean Jordan algebra stems from the likewise-analogous characteristic polynomial of its elements, whose degree is called the rank of the algebra. As a prerequisite for the spectral decomposition, we derive an algorithm that computes the rank of a Euclidean Jordan algebra and allows us to construct the characteristic polynomials of its elements.

Keywords: Euclidean Jordan algebra, characteristic polynomial, spectral decomposition, rank, regular element

Category 1: Linear, Cone and Semidefinite Programming

Category 2: Convex and Nonsmooth Optimization (Convex Optimization )

Citation: July 3, 2021

Download: [PDF]

Entry Submitted: 07/03/2021
Entry Accepted: 07/06/2021
Entry Last Modified: 07/06/2021

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