Norm Hull of Vectors and Matrices

Chi-Kwong Li; Nam-Kiu Tsing; Fuzhen Zhang

doi:10.1016/S0024-3795(96)00099-7

Norm Hull of Vectors and Matrices

Chi-Kwong Li
, Nam-Kiu Tsing
, Fuzhen Zhang

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

<p> 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 &spar;y&spar; ≤ &spar;x&spar; for all &spar; · &spar; ∈ 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</p>

Original language	American English
Journal	Linear Algebra and its Applications
Volume	257
DOIs	https://doi.org/10.1016/S0024-3795(96)00099-7
State	Published - May 1 1997

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Mathematics

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title = "Norm Hull of Vectors and Matrices",

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 \&spar;y\&spar; \≤ \&spar;x\&spar; for all \&spar; \· \&spar; \∈ 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",

author = "Chi-Kwong Li and Nam-Kiu Tsing and Fuzhen Zhang",

year = "1997",

month = may,

day = "1",

doi = "10.1016/S0024-3795(96)00099-7",

language = "American English",

volume = "257",

journal = "Linear Algebra and its Applications",

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T1 - Norm Hull of Vectors and Matrices

AU - Li, Chi-Kwong

AU - Tsing, Nam-Kiu

AU - Zhang, Fuzhen

PY - 1997/5/1

Y1 - 1997/5/1

N2 - 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 &spar;y&spar; ≤ &spar;x&spar; for all &spar; · &spar; ∈ 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

AB - 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 &spar;y&spar; ≤ &spar;x&spar; for all &spar; · &spar; ∈ 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

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

UR - http://www.sciencedirect.com/science/article/pii/S0024379596000997

U2 - 10.1016/S0024-3795(96)00099-7

DO - 10.1016/S0024-3795(96)00099-7

M3 - Article

SN - 0024-3795

VL - 257

JO - Linear Algebra and its Applications

JF - Linear Algebra and its Applications

ER -

Norm Hull of Vectors and Matrices

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