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Gradient

In vector calculus, the gradient of a scalar-valued differentiable function f {\displaystyle f} of several variables is the vector field (or vector-valued function) ∇ f {\displaystyle \nabla f} whose value at a point p {\displaystyle p} gives the direction and the rate of fastest increase. The gradient transforms like a vector under change of basis of the…

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Overview

Motivation

Notation

Definition

Relationship with derivative

Further properties and applications

Generalizations

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Map overview Semantic statistics

Gradient

Nodes105
Edges104
Triples76
Avg. degree1.98
Density0.019048
Components1

How this topic connects Entity context

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Gradient

Top relations

related to Jacobian · 11
Gradient → Banach, Euclidean, Explicitly, Fréchet, Jacobian, Rm, Rn, Suppose, The, The Jacobian, Then
related to External links · 8
Gradient → EMS Press, Encyclopedia, Eric, Khan Academy, Kuptsov, Mathematics, MathWorld, Weisstein
related to Riemannian manifolds · 7
Gradient → Bigg, For, In, Riemannian, Rn, So, Xj
related to background · 6
Gradient → As, Fréchet, If, Let, Rn, Thus
see also · 6
Gradient → Circulation, Curl, Four-vector, Mathematical, Matrix, Vector
is a · 5
Gradient → direction in which the function increases most quickly from p, element of the tangent space at a point, same as taking the directional derivative along the vector.If R n, tangent vector, zero vector is known as a stationary point
related to General coordinates · 5
Gradient → Here, Note, The, Using Einstein, We
related to Level sets · 4
Gradient → For, If, It, The
related to Notation · 4
Gradient → Einstein, It, The, Written
related to Cartesian coordinates · 3
Gradient → Cartesian, Euclidean, In

Important terminology Word statistics

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Important terminology

displaystyle vector nabla function point derivative partial direction frac differentiable mathbf df defined differential field coordinate tangent isbn given mathbb

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Gradientis adirection in which the function increases most quickly from p0.90text
Gradientis azero vector is known as a stationary point0.90text
Gradientis atangent vector0.90text
Gradientis aelement of the tangent space at a point0.90text
Gradientis asame as taking the directional derivative along the vector.If R n0.90text
timeinstance ofsee relationship with derivative.When a function also depends on a parameter0.80text
the gradient often refers simply to the vector of its spatial derivatives onlyinstance ofsee relationship with derivative.When a function also depends on a parameter0.80text
Gradientrelated to backgroundLet0.60section
Gradientrelated to backgroundRn0.60section
Gradientrelated to backgroundIf0.60section
Gradientrelated to backgroundFréchet0.60section
Gradientrelated to backgroundThus0.60section

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    Min side: 3
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