Optimization Online


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

Modify/Update this entry

  Visitors Authors More about us Links
  Subscribe, Unsubscribe
Digest Archive
Search, Browse the Repository


Coordinator's Board
Classification Scheme
Give us feedback
Optimization Journals, Sites, Societies
Mathematical Optimization Society