Norm hull of vectors and matrices Original Research Article

Let V be a real or complex finite-dimensional vector space, and let image be a set of norms on V. The norm hull of a vector x set membership, variant V with respect to image is the set of vectors y set membership, variant V that satisfy short parallelyshort parallel ≤ short parallelxshort parallel for all short parallel · short parallel set membership, variant N. We study and give characterization of the norm hull for some sets of well-known norms on general vector spaces, and for the set of algebra norms and the set of induced norms on the algebra of n × n real or complex matrices.