论文标题
Zeon矩阵的光谱定理
A Spectral Theorem for Zeon Matrices
论文作者
论文摘要
在本文中，建立了具有（复杂）Zeon条目的矩阵的光谱定理。特别是，当$ a $是一个$ m $ a $时，$ a $ a $ hexexhoind矩阵的特征多项式$χ_a（u）$ $ apl zeon algebra $ {\ mathbb {c} \ mathfrak {z}}} _ n $ $ m $ $ $独立归一化Zeon eigenVectors $ v_1，\ ldots，v_m $，使得$ a = \ bigoplus_ {j = 1}^mλ_jπ_j$，其中$π_j= v_j {v_j {v_j}^†$是Zeon sumpodule $ $ {\ rm span} \ {v_j \} $ for $ j = 1，\ ldots，m $。
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 $χ_A(u)$ "splits" over the zeon algebra ${\mathbb{C}\mathfrak{Z}}_n$, there exist $m$ spectrally simple eigenvalues $λ_1, \ldots, λ_m$ and $m$ 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 $j=1, \ldots, m$.
