What question did this study set out to answer?

The aim is to analyze the spectral properties of matrices with zeon entries and establish eigenvector relationships.

July 3, 2026Galois Journal of Algebra1 citationsOpen Access

A Spectral Theorem for Zeon Matrices

GSG. Stacey StaplesSouthern Illinois University Edwardsville

Key Points

The aim is to analyze the spectral properties of matrices with zeon entries and establish eigenvector relationships.
Investigated properties of m × m self-adjoint zeon matrices
Examined the characteristic polynomial with zeon algebra
Demonstrated the existence of linearly independent normalized zeon eigenvectors
Established that for self-adjoint matrices with spectrally simple zeros, there are m linearly independent normalized zeon eigenvectors.
Identified the relationship A = ⨁j=1m λjπj with defined rank-one projections.

Abstract

In this paper, spectral properties of matrices with (complex) zeon entries are investigated. It is shown that when A is an m × m self-adjoint matrix whose characteristic polynomial χA (u) has m "spectrally simple" zeros λ1, …, λm in the zeon algebra C𝒵, there exist m linearly independent normalized zeon eigenvectors v1, …, vm such that A = ⨁j=1m λjπj, where πj = vjvj† is a rank-one projection onto the zeon submodule spanvj for j = 1, …, m.

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