A Spectral Theorem for Zeon Matrices
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866912631850270720 |
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| author | Staples, G. Stacey |
| author_facet | Staples, G. Stacey |
| contents | 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 $j=1, \ldots, m$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2201_09321 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | A Spectral Theorem for Zeon Matrices Staples, G. Stacey Rings and Algebras Spectral Theory 15B33, 15A09, 05C50, 05E15, 81R05 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 $j=1, \ldots, m$. |
| title | A Spectral Theorem for Zeon Matrices |
| topic | Rings and Algebras Spectral Theory 15B33, 15A09, 05C50, 05E15, 81R05 |
| url | https://arxiv.org/abs/2201.09321 |