Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Spectral Theorem for Zeon Matrices   In this paper, a spectral theorem for matrices with (complex) zeon entries is
established. In particular, it is shown that when $A$ is an $m\times m$
self-adjoint matrix whose characteristic polynomial $\chi_A(u)$ "splits" over
the zeon algebra ${\mathbb{C}\mathfrak{Z}}_n$, there exist $m$ spectrally
simple eigenvalues $\lambda_1, \ldots, \lambda_m$ and $m$ linearly independent
normalized zeon eigenvectors $v_1, \ldots, v_m$ such that $A=\bigoplus_{j=1}^m
\lambda_j\pi_j$, where $\pi_j=v_j{v_j}^\dag$ is a rank-one projection onto the
zeon submodule ${\rm span}\{v_j\}$ for $j=1, \ldots, m$.

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The categories of this paper are: adap-org
12
The categories of this paper are: nucl-th
33
The categories of this paper are: plasm-ph
9
The categories of this paper are: nlin
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The categories of this paper are: nucl-ex
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The categories of this paper are: eess
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The categories of this paper are: ao-sci
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The categories of this paper are: mtrl-th
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-lat
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The categories of this paper are: quant-ph
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The categories of this paper are: cmp-lg
5
The categories of this paper are: gr-qc
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The categories of this paper are: chem-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: solv-int