A Spectral Theorem for Zeon Matrices

Abstract

In this paper, a spectral theorem for matrices with (complex) zeon entries is established. In particular, it is shown that when A is an m × m self-adjoint matrix whose characteristic polynomial χA(u) splits over the zeon algebra CZ n , there exist m spectrally simple eigenvalues λ1, . . . , λm and m linearly independent normalized zeon eigenvectors v1, . . . , vm such that A = m j=1 λjπj, where πj = vjvj † is a rank-one projection onto the zeon submodule span{vj} for j = 1, . . . , m.