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Bivector

In mathematics, a bivector or 2-vector is a quantity in exterior algebra or geometric algebra that extends the idea of scalars and vectors. Considering a scalar as a degree-zero quantity and a vector as a degree-one quantity, a bivector is of degree two. Bivectors have applications in many areas of mathematics and physics. They are related to complex…

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Overview

History

Derivation

Properties

Two dimensions

Three dimensions

Four dimensions

Higher dimensions

Projective geometry

General references

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Bivector

Nodes149
Edges148
Triples187
Avg. degree1.99
Density0.013423
Components1

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Bivector

Top relations

related to General references · 29
Bivector → An Object-Oriented Approach, Anthony Lasenby, Cambridge, Cambridge University Press, Chris Doran, Clifford, Computer Science, Daniel, Dorst, Dover Publications, Fontijne, Geometric Algebra, Geometric Integration Theory, Geometry, Hassler, ISBN, Leo, Lounesto, Mann, Morgan Kaufmann
related to history · 26
Bivector → Clifford, David Hestenes, English, German, Gibbs, Grassmann, Grassmann's, Hamilton, Hamilton's, Henry Forder, Hermann Grassmann, In, Ireland, It, Its, Josiah Willard Gibbs, Just, Lectures, Oliver Heaviside, Quaternions
related to Axial vectors · 9
Bivector → Alternately, Axial, Cl3, Examples, Hodge, More, Note, Quantities, The
related to Projective geometry · 9
Bivector → Cln, For, Geometric, Non-zero, Rn, RPn, The, This, Two
related to Simple bivectors in 4D · 8
Bivector → Cl4, In, R2, R3, R4, The, There, This
related to Spacetime rotations · 8
Bivector → Cl3, Euclidean, It, Minkowski, Note, Spacetime, That, The
related to Orthogonality · 7
Bivector → For, Hodge, In, Normal, There, This, We
related to Quaternions · 7
Bivector → Bivectors, Cl, In, It, Other, The, This
related to General bivectors and matrices · 6
Bivector → B12e12, B23e23, B31e31, Bivectors, For, This
related to Higher dimensions · 6
Bivector → As, Cln, For, Rn, So, The

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Important terminology

bivectors dimensions vector two vectors geometric product algebra three simple space exterior rotation plane scalar rotations magnitude complex written used

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Bivectoris azero bivector which as an element of the geometric algebra equals the scalar zero.Unit bivectorsA unit bivector is one with unit magnitude0.90text
Bivectoris asum of at most two exterior products0.90text
Bivectoris azero bivector which as an element of the geometric algebra equals the scalar zero0.90text
Bivectoris abivector0.90text
e12instance ofThere are bivectors0.80text
the angular velocity tensorinstance ofBut it is also used with other bivectors0.80text
the electromagnetic tensorinstance ofBut it is also used with other bivectors0.80text
respectively a 3instance ofBut it is also used with other bivectors0.80text
Bivectorrelated to Axial vectorsThe0.60section
Bivectorrelated to Axial vectorsAxial0.60section
Bivectorrelated to Axial vectorsExamples0.60section
Bivectorrelated to Axial vectorsQuantities0.60section

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