منابع مشابه
Inverse Expander Mixing for Hypergraphs
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15 صفحه اولDiscrete Norms of a Matrix and the Converse to the Expander Mixing Lemma
We define the discrete norm of a complex m× n matrix A by ‖A‖∆ := max 06=ξ∈{0,1}n ‖Aξ‖ ‖ξ‖ , and show that c √ log h(A) + 1 ‖A‖ ≤ ‖A‖∆ ≤ ‖A‖, where c > 0 is an explicitly indicated absolute constant, h(A) = √ ‖A‖1‖A‖∞/‖A‖, and ‖A‖1, ‖A‖∞, and ‖A‖ = ‖A‖2 are the induced operator norms of A. Similarly, for the discrete Rayleigh norm ‖A‖P := max 06=ξ∈{0,1} 06=η∈{0,1} |ξAη| ‖ξ‖‖η‖ we prove the esti...
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2016
ISSN: 1077-8926
DOI: 10.37236/5283