Positivity in complex spaces and its application to Gershgorin discs

Summary The classical proof that a separated Gershgorin disc contains an eigenvalue uses a continuity argument which is not applicable to Bauers generalized Gershgorin discs. In this paper the concept of positivity, generalized to complex vector spaces, is used to establish Gershgorins result and to improve the corresponding result for Bauers generalization.Dedicated to Professor F.L. Bauer on the occasion of his 60th birthday