## Mathematics Faculty Articles

# Norm Hull of Vectors and Matrices

## Document Type

Article

## Publication Date

5-1-1997

## Publication Title

Linear Algebra and its Applications

## ISSN

0024-3795

## Volume

257

## First Page

1

## Last Page

27

## Abstract

Let V be a real or complex finite-dimensional vector space, and let be a set of norms on V. The norm hull of a vector x ∈ V with respect to is the set of vectors y ∈ V that satisfy ∥y∥ ≤ ∥x∥ for all ∥ · ∥ ∈ 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

## NSUWorks Citation

Li, Chi-Kwong; Tsing, Nam-Kiu; and Zhang, Fuzhen, "Norm Hull of Vectors and Matrices" (1997). *Mathematics Faculty Articles*. 76.

https://nsuworks.nova.edu/math_facarticles/76

## DOI

10.1016/S0024-3795(96)00099-7

COinS

## Comments

Under an Elsevier user license