Sparad:
| Huvudupphovsman: | |
|---|---|
| Materialtyp: | Preprint |
| Publicerad: |
2022
|
| Ämnen: | |
| Länkar: | https://arxiv.org/abs/2201.09321 |
| Taggar: |
Lägg till en tagg
Inga taggar, Lägg till första taggen!
|
Innehållsförteckning:
- In this paper, spectral properties of matrices with (complex) zeon entries are investigated. It is shown that when $A$ is an $m\times m$ self-adjoint matrix whose characteristic polynomial $χ_A(u)$ has $m$ ``spectrally simple'' zeros $λ_1, \ldots, λ_m$ in the zeon algebra ${\mathbb{C}\mathfrak{Z}}$, there exist $m$ linearly independent normalized zeon eigenvectors $v_1, \ldots, v_m$ such that $A=\bigoplus_{j=1}^m λ_jπ_j$, where $π_j=v_j{v_j}^†$ is a rank-one projection onto the zeon submodule ${\rm span}\{v_j\}$ for $j=1, \ldots, m$.