Numerical radius and zero pattern of matrices
arXiv:math/0703177 · doi:10.1016/j.jmaa.2007.04.042
Abstract
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.