The Weyr Characteristic of the Inverse, the Adjoint and the Orthogonal of a Linear Relation

Abstract The well-known Weyr characteristic for matrices, which counts the amount of linearly independent Jordan chains of a certain length, generalizes to linear relations in finite dimensional spaces. The Weyr characteristic of a linear relation consists of three finite sequences counting different types of linearly independent chains. Given a linear relation, the Weyr characteristics of its inverse, its adjoint, and its orthogonal complement are computed.