A Spectral Theorem for Zeon Matrices

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.