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Matrix norm

In mathematics, a norm is a function from a vector space to non-negative real numbers that satisfies certain axioms. A matrix norm is a norm defined on a vector space of matrices. As for every norm, a matrix norm defines a distance, the distance between two matrices being the norm of their difference. The specificity of matrix norms is that they may…

"Entry-wise" matrix norms, Overview & Matrix norms induced by vector norms

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Overview

Preliminaries

Possible properties

Matrix norms induced by vector norms

"Entry-wise" matrix norms

Schatten norms

Cut norms

Equivalence of norms

Bibliography

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Matrix norm

Nodes72
Edges71
Triples33
Avg. degree1.97
Density0.027778
Components1

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Matrix norm

Top relations

related to Cut norms · 6
Matrix norm → Another, Box, Equivalent, Grothendieck, Km, The
related to Consistent and compatible norms · 4
Matrix norm → All, Also, Ax, In
related to Matrix norms induced by vector α- and β-norms · 4
Matrix norm → Ax, In, Suppose, We
related to Square matrices · 4
Matrix norm → AB, Moreover, Suppose, Then
is a · 3
Matrix norm → norm defined on a vector space of matrices, norm on K m, spectral norm
related to Equivalence of norms · 3
Matrix norm → For, In, This
related to Monotone norms · 3
Matrix norm → Loewner, The Frobenius, Thus
related to Preliminaries · 3
Matrix norm → Given, K-vector, The
related to Unitary invariance · 3
Matrix norm → Px, That, UAV

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Important terminology

norm displaystyle matrix norms vector leq matrices operator induced alpha times cdot beta called may spectral max space singular frobenius

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Matrix normis anorm defined on a vector space of matrices0.90text
Matrix normis anorm on K m0.90text
Matrix normis aspectral norm0.90text
Matrix normrelated to Consistent and compatible normsAx0.60section
Matrix normrelated to Consistent and compatible normsIn0.60section
Matrix normrelated to Consistent and compatible normsAll0.60section
Matrix normrelated to Consistent and compatible normsAlso0.60section
Matrix normrelated to Cut normsAnother0.60section
Matrix normrelated to Cut normsThe0.60section
Matrix normrelated to Cut normsBox0.60section
Matrix normrelated to Cut normsKm0.60section
Matrix normrelated to Cut normsEquivalent0.60section

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