Linear G-Functions

Let {dijk}i≠j be a given set of n2(n − 1) nonnegative numbers. We characterize those sets {dijk}i≠j for which the following statement is true: for every complex matrix A, every eigenvalue of A lies in the union of the n disks [formula omitted]. Many generalizations of Gerschgorin's theorem are shown to be consequences. © 1975, Taylor & Francis Group, LLC. All rights reserved.