Clifford spectrum of three 2 by 2 matrices

TL;DR

This paper proves the nonemptiness of the Clifford spectrum for three 2x2 matrices, describes its structure via level curves, and explores implications for larger matrices and infinite-dimensional operators.

Contribution

It establishes the nonemptiness of the Clifford spectrum for three 2x2 matrices and analyzes its structure, extending the understanding to higher dimensions and infinite spaces.

Findings

Clifford spectrum for three 2x2 matrices is nonempty

Structure described by moving level curves

Implications for larger matrices and infinite-dimensional operators

Abstract

We prove that the Clifford spectrum associated to three 2 by 2 matrices is nonempty. The structure of Clifford is described in terms "moving" level curves. We discuss some implication of a conjecture formulated for arbitrary size n by n of three matrices and give an example in the case of three self-adjoint operators in the infinite dimensional Hilbert space.