Abstract

We derive upper bounds for the spectral radius of the n×n Hilbert matrix. The key idea is to write the Hilbert matrix as integral operator with positive kernel function and then to use a Wielandt-type min-max principle for the spectral radius. Choosing special trial functions yields a new bound that improves the best bound known heretofore.

Keywords

Hilbert matrix, Hilbert inequality, spectral radius, Wielandt min-max principle, integral operator

Mathematical Subject Classification

Primary: 15A42, 15A60, 47G10

Authors