Maximizing the numerical radii of matrices by permuting their entries
Wai-Shun Cheung, Chi-Kwong Li · Linear and Multilinear Algebra · 2013
Let be an complex matrix such that every row and every column has at most one non-zero entry. We determine permutations of the non-zero entries of so that the resulting matrix has maximum numerical radius. Extension of the results to operators acting on separable Hilbert spaces are also obtained. Related results and additional problems are also mentioned.