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Tensor

In mathematics, a tensor is an algebraic object that describes a multilinear relationship between sets of algebraic objects associated with a vector space. Tensors may map between different objects such as vectors, scalars, and even other tensors. There are many types of tensors, including scalars and vectors (which are the simplest tensors), dual…

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Overview

Definition

Tensors in infinite dimensions

History

Examples

Properties

Notation

Operations

Applications

Generalizations

Foundational

General

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Map overview Semantic statistics

Tensor

Nodes222
Edges221
Triples133
Avg. degree1.99
Density0.009009
Components1

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Tensor

Top relations

related to history · 12
Tensor → Carl Friedrich Gauss, Gregorio Ricci-Curbastro, In Ricci's, It, Josiah Willard Gibbs, Methods, Méthodes, Ricci-Curbastro, The, Tullio Levi-Civita's, William Rowan Hamilton, Woldemar Voigt
related to Tensors in infinite dimensions · 11
Tensor → Another, Banach, Constructions, For, Fréchet, Hilbert, In, One, Tensors, The, This
related to As multidimensional arrays · 7
Tensor → For, Just, The, They, Thus, Tij, Whether
related to Continuum mechanics · 7
Tensor → If, Important, In, The, This, Thus, Within
related to Computer vision and optics · 6
Tensor → If, Taylor, Tensors, The, This, To
related to Examples · 6
Tensor → An, Cauchy, For, In, The, This
related to Properties · 6
Tensor → Assuming, Because, Changing, Compare, For, The
related to Spinors · 6
Tensor → However, It, Other, Spinors, This, When
related to As multilinear maps · 5
Tensor → Although, In, More, One, The
related to Contraction · 5
Tensor → Components, For, It, The, When

Important terminology Word statistics

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Important terminology

tensors vector basis product components linear space transformation array displaystyle covariant index general type example contravariant matrix indices multilinear one

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Tensoris aalgebraic object that describes a multilinear relationship between sets of algebraic objects associated with a vector space0.90text
Tensoris adot product0.90text
Tensoris asum of these two numbers.The order0.90text
Tensoris asame thing as a multidimensional array0.90text
vectorsinstance ofTensors may map between different objects0.80text
scalarsinstance ofTensors may map between different objects0.80text
and even other tensorsinstance ofTensors may map between different objects0.80text
the dot productinstance ofand even some operations0.80text
mechanicsinstance ofbecause they provide a concise mathematical framework for formulating and solving physics problems in areas0.80text
continuum mechanicsinstance ofAlbert EinsteinEinstein's general relativity was formulated in the language of tensors.Tensors and tensor fields were also found to be useful in other fields0.80text
metric tensorsinstance ofSome well-known examples of tensors in differential geometry are quadratic forms0.80text
and the Riemann curvature tensorinstance ofSome well-known examples of tensors in differential geometry are quadratic forms0.80text

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