Matrix Quasinorms Induced by Maximal and Minimal Vector Norms

Abstract

In the set of all vector norms in Cn, there exist maximal and minimal complex norms which coincide with the real Euclidean norm in Rn. The purpose of this paper is to introduce new quasinorms defined on complex matrices. These two matrix quasinorms are induced by maximal and minimal complex vector norms. We also prove the dual relation between these two quasinorms.