Numerical radius and zero pattern of matrices
classification
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math.FA
keywords
matricesnumericalboundscliquecombinatorialconciseeuclidianextremal
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We give tight upper bounds on the numerical range of square matrices in terms of their Frobenius (Euclidian) norm and a combinatorial parameter similar to the clique number of graphs. Our results imply a concise form of the fundamental theorem of Turan in extremal graph theory.
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