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Cross product

In mathematics, the cross product or vector product (occasionally directed area product, to emphasize its geometric significance) is a binary operation on two vectors in a three-dimensional oriented Euclidean vector space (named here E {\displaystyle E} ), and is denoted by the symbol × {\displaystyle \times } . Given two linearly independent vectors a…

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Overview

Definition

Names and origin

Computing

Properties

Lagrange's identity

Alternative ways to compute

Applications

As an external product

Generalizations

History

Bibliography

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Map overview Semantic statistics

Cross product

Nodes174
Edges173
Triples118
Avg. degree1.99
Density0.011494
Components1

How this topic connects Entity context

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Cross product

Top relations

related to External links · 17
Cross product → Berkeley, California, Cross, Cross-Products, EMS Press, Encyclopedia, Euclidean, Kahan, Mathcentre, Mathematics, PDF, Rotations, Space, Syracuse University, The, UK, University
related to history · 7
Cross product → Given, Hamilton's, In, James Clerk Maxwell, Joseph-Louis Lagrange, R3, William Rowan Hamilton
related to Lie algebra · 7
Cross product → For, Heisenberg, In, Jacobi, Lie, Many Lie, The
related to As an external product · 6
Cross product → Given, Hodge, In, It, The, This
related to Direction · 6
Cross product → As, By, Conventionally, The, Then, Using
related to Exterior product · 6
Cross product → As, Hodge, In, The, The Hodge, There
related to Names and origin · 6
Cross product → Hamilton, In, Josiah Willard Gibbs, Oliver Heaviside, The, William Rowan Hamilton
related to External product · 5
Cross product → As, Hodge, In, So, This
related to Alternative formulation · 4
Cross product → Gram, Namely, The, This
related to Index notation for tensors · 4
Cross product → Eijk, Leftrightarrow, Levi-Civita, The

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Important terminology

product cross displaystyle vectors vector times mathbf two dimensions algebra defined three begin end dot used matrix given also right

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Cross productis aalgebra over the real numbers0.90text
Cross productis apseudovector.In connection with the cross product0.90text
Cross productis avector0.90text
multi-dimensional space-timeinstance ofso it is not used in mathematical physics to represent quantities0.80text
a tetrahedron or parallelepiped.Angular momentuminstance ofThe cross product is used in calculating the volume of a polyhedron0.80text
torqueThe angular momentum L of a particle about a given origin is defined asinstance ofThe cross product is used in calculating the volume of a polyhedron0.80text
a tetrahedron or parallelepipedinstance ofThe cross product is used in calculating the volume of a polyhedron0.80text
Cross producthas applicationThe0.60section
Cross producthas applicationFor0.60section
Cross productrelated to Algebraic propertiesIf0.60section
Cross productrelated to Algebraic propertiesThe0.60section
Cross productrelated to Alternative formulationThe0.60section

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