| A study of Eaton triples is presented in which a generalization of the Dominance Theorem of Ky Fan on the unitarily invariant norm is obtained. The results of Zietak on the characterization of the set of dual matrices of a given matrix and the faces of the unit ball, both with respect to a unitarily invariant norm, are also extended in the context of Eaton triples. The notion of dual matrices of a given matrix A with respect to a unitarily invariant norm is related to the subdifferential of the norm at A . A generalization of So's characterization of the extreme points of the unit ball is given. |
