Eigenspace conditions for homomorphic sensing. (arXiv:1812.07966v1 [math.CO])

Given two endomorphisms $\tau_1,\tau_2$ of $\mathbb{C}^m$ with $m \ge 2n$ and a general $n$-dimensional subspace $\mathcal{V} \subset \mathbb{C}^m$, we provide eigenspace conditions under which $\tau_1(v_1)=\tau_2(v_2)$ for $v_1,v_2 \in \mathcal{V}$ can only be true if $v_1=v_2$. As a special case, we recover the result of Unnikrishnan et al. in which $\tau_1,\tau_2$ are permutations composed with coordinate projections.查看全文

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