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Isometry

In mathematics, an isometry (or congruence, or congruent transformation) is a distance-preserving transformation between metric spaces, usually assumed to be bijective. The word isometry is derived from the Ancient Greek: ἴσος isos meaning "equal", and μέτρον metron meaning "measure". If the transformation is from a metric space to itself, it is a kind…

Standards, Definition & Isometries between normed spaces

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Overview

Introduction

Definition

Isometries between normed spaces

Manifold

Generalizations

Bibliography

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Map overview Semantic statistics

Isometry

Nodes90
Edges89
Triples55
Avg. degree1.98
Density0.022222
Components1

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Isometry

Top relations

related to Introduction · 9
Isometry → Banach, Cauchy, Euclidean, For, Given, In, Isometries, Other, The
related to Isometries between normed spaces · 8
Isometry → If, Let, Mazur, Stefan Banach, The, Then, Theorem, Ulam
see also · 8
Isometry → Angular, Banach, Homeomorphism, Mathematical, Myers, Quarles, Semidefinite, Steenrod
related to Definition · 7
Isometry → An, Clearly, Equivalently, Let, Riemannian, Then, This
related to Manifold · 6
Isometry → An, Riemannian, Rm, The, Thus, When
related to Properties · 6
Isometry → Killing, Lie, Riemannian, Steenrod, The Myers, When
related to Generalizations · 5
Isometry → Given, Hausdorff, One, Quasi-isometry, The
is a · 3
Isometry → linear map A, map which preserves the lengths of curves, transformation which maps elements to the same or another metric space such that the distance between the image elements in the new metric space is equal to the distance between…
related to Linear isometry · 3
Isometry → Given, Linear, They

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Important terminology

metric displaystyle spaces map space isometries linear also vector isbn called riemannian group bijective transformation two isometric second manifold oclc

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Isometryis atransformation which maps elements to the same or another metric space such that the distance between the image elements in the new metric space is equal to the distance between…0.90text
Isometryis amap which preserves the lengths of curves0.90text
Isometryis alinear map A0.90text
Isometryrelated to DefinitionLet0.60section
Isometryrelated to DefinitionAn0.60section
Isometryrelated to DefinitionThis0.60section
Isometryrelated to DefinitionClearly0.60section
Isometryrelated to DefinitionRiemannian0.60section
Isometryrelated to DefinitionThen0.60section
Isometryrelated to DefinitionEquivalently0.60section
Isometryrelated to GeneralizationsGiven0.60section
Isometryrelated to GeneralizationsHausdorff0.60section

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