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Legendre transformation

In mathematics, the Legendre transformation (or Legendre transform), first introduced by Adrien-Marie Legendre in 1787 when studying the minimal surface problem, is an involutive transformation on real-valued functions that are convex on a real variable. Specifically, if a real-valued multivariable function is convex on one of its independent real…

Applications, Definition & Legendre transformation in more than one dimension

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Overview

Definition

Properties

Identities

  • Above Legendre transformation

Examples

Behavior of differentials under Legendre transforms

Applications

Geometric interpretation

Legendre transformation in more than one dimension

Legendre transformation on manifolds

Further properties

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Map overview Semantic statistics

Legendre transformation

Nodes130
Edges129
Triples77
Avg. degree1.98
Density0.015385
Components1

How this topic connects Entity context

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Legendre transformation

Top relations

related to Properties · 12
Legendre transformation → Applying, By, For, Inverse, Legendre, Let, Note, Proof, The Legendre, Then, This, Thus
related to Example 1 · 10
Legendre transformation → As, By, Consider, From, Legendre, The, This, Thus, To, We
related to Further reading · 10
Legendre transformation → Archived, Elements, Frank, Hugo, Legendre, Legendre-Fenchel, Nielsen, PDF, Retrieved, Touchette
related to Probability theory · 10
Legendre transformation → An, Cramér's, For, Hence, If, In, Lambda, Legendre, Markov's, Since
related to Legendre transformation on manifolds · 9
Legendre transformation → As, Here, In, Lagrangian, Let, The, The Legendre, TM, We
related to Example 4 · 6
Legendre transformation → Clearly, Hence, Legendre, One, The, Then
related to Microeconomics · 6
Legendre transformation → For, Legendre, Let, P-C, PQ-C, We
is a · 4
Legendre transformation → application of the duality relationship between points and lines, homogeneous function of degree s, involution, one originally introduced by Legendre in his work in 1787
related to Geometric interpretation · 3
Legendre transformation → For, Legendre, The
related to Scaling properties · 3
Legendre transformation → For, Rightarrow, The Legendre

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Important terminology

displaystyle function legendre transform convex transformation textstyle frac left right -1 variables one derivative variable differentiable mathbb defined -f mathbf

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Legendre transformationis aapplication of the duality relationship between points and lines0.90text
Legendre transformationis aone originally introduced by Legendre in his work in 17870.90text
Legendre transformationis ainvolution0.90text
Legendre transformationis ahomogeneous function of degree s0.90text
Legendre transformationrelated to Definition in n-dimensional real spaceThe0.60section
Legendre transformationrelated to Definition in n-dimensional real spaceThe Legendre0.60section
Legendre transformationrelated to Definition in physical contextsIn0.60section
Legendre transformationrelated to Definition in physical contextsLegendre0.60section
Legendre transformationrelated to Example 1Consider0.60section
Legendre transformationrelated to Example 1From0.60section
Legendre transformationrelated to Example 1Legendre0.60section
Legendre transformationrelated to Example 1To0.60section

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