Surfaces and hypersurfaces as the joint spectrum of matrices

2019/11/02 by Patrick H. DeBonis, DeBonis, Patrick H., Terry A. Loring +3
Mathematics · #Advanced Topics in Algebra #Algebraic and Geometric Analysis #FOS: Mathematics #Geometric and Algebraic Topology #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.1911.00751

openalex publication_date 2019/11/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The Clifford spectrum is an elegant way to define the joint spectrum of several Hermitian operators. While it has been know that for examples as small as three 2-by-2 matrices the Clifford spectrum can be a two-dimensional manifold, few concrete examples have been investigated. Our main goal is to generate examples of the Clifford spectrum of three or four matrices where, with the assistance of a computer algebra package, we can calculate the Clifford spectrum.

Related

• Notions of determinant, spectrum, and Hermitian conjugation of Clifford algebra elements
• Introductory Clifford Analysis
• The spectral theorem for normal operators on a Clifford module
• Unitary canonical forms over Clifford algebras, and an observed unification of some real-matrix decompositions
• Geometric spectral theory for compact operators