Gershgorin domains for partitioned matrices

Abstract

Inclusion domains for the eigenvalues of a partitioned matrix are specified in terms of perturbations of its diagonal blocks. The size of such perturbations is measured using the Kantorovitch-Robert-Deutsch vectorial norms. The inclusion domains obtained thereby are compared with inclusion domains otherwise obtainable. A few new properties of vectorial norms are proved as well. A result of Bonsall, Schneider, Strang and Ljubic is generalized.