A Spectral Theorem for Zeon Matrices
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 span{vj} for j = 1, …, m.
Fields of Study & Subjects
Graph theory and applications
Matrix Theory and Algorithms
Spectral Theory in Mathematical Physics
Publication details
- Journal / source
- Galois Journal of Algebra
- Publisher
- Interaction Scientifique
- Volume
- 2
- Issue
- 2
- Pages
- 1–27
- Publication date
- 30 June 2026
- Language
- EN