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- Bivector abstract "In mathematics, a bivector or 2-vector is a quantity in exterior algebra or geometric algebra that extends the idea of scalars and vectors. If a scalar is considered an order zero quantity, and a vector is an order one quantity, then a bivector can be thought of as being of order two. Bivectors have applications in many areas of mathematics and physics. They are related to complex numbers in two dimensions and to both pseudovectors and quaternions in three dimensions. They can be used to generate rotations in any dimension, and are a useful tool for classifying such rotations. They also are used in physics, tying together a number of otherwise unrelated quantities.Bivectors are generated by the exterior product on vectors: given two vectors a and b, their exterior product a ∧ b is a bivector, as is the sum of any bivectors. Not all bivectors can be generated as a single exterior product. More precisely, a bivector that can be expressed as an exterior product is called simple; in up to three dimensions all bivectors are simple, but in higher dimensions this is not the case. The exterior product is antisymmetric, so b ∧ a is the negation of the bivector a ∧ b, producing the opposite orientation, and a ∧ a is the zero bivector. Geometrically, a simple bivector can be interpreted as an oriented plane segment, much as vectors can be thought of as directed line segments. The bivector a ∧ b has a magnitude equal to the area of the parallelogram with edges a and b, has the attitude of the plane spanned by a and b, and has orientation being the sense of the rotation that would align a with b. It does not have a definite location or position.".
- Bivector thumbnail Wedge_product.JPG?width=300.
- Bivector wikiPageExternalLink books?id=-1-zRTeCXwgC&pg=PA31.
- Bivector wikiPageExternalLink books?id=kOsybQWDK4oC.
- Bivector wikiPageExternalLink books?id=nZ6MsVIdt88C&pg=PA11.
- Bivector wikiPageID "884040".
- Bivector wikiPageRevisionID "597120407".
- Bivector hasPhotoCollection Bivector.
- Bivector subject Category:Clifford_algebras.
- Bivector subject Category:Geometric_algebra.
- Bivector subject Category:Multilinear_algebra.
- Bivector subject Category:Tensors.
- Bivector subject Category:Vector_calculus.
- Bivector type Abstraction100002137.
- Bivector type Algebra106012726.
- Bivector type CliffordAlgebras.
- Bivector type Cognition100023271.
- Bivector type Concept105835747.
- Bivector type Content105809192.
- Bivector type Discipline105996646.
- Bivector type Idea105833840.
- Bivector type KnowledgeDomain105999266.
- Bivector type Mathematics106000644.
- Bivector type PsychologicalFeature100023100.
- Bivector type PureMathematics106003682.
- Bivector type Quantity105855125.
- Bivector type Science105999797.
- Bivector type Tensor105864481.
- Bivector type Tensors.
- Bivector type Variable105857459.
- Bivector comment "In mathematics, a bivector or 2-vector is a quantity in exterior algebra or geometric algebra that extends the idea of scalars and vectors. If a scalar is considered an order zero quantity, and a vector is an order one quantity, then a bivector can be thought of as being of order two. Bivectors have applications in many areas of mathematics and physics. They are related to complex numbers in two dimensions and to both pseudovectors and quaternions in three dimensions.".
- Bivector label "Bivecteur".
- Bivector label "Bivector".
- Bivector sameAs 2-διάνυσμα.
- Bivector sameAs Bivecteur.
- Bivector sameAs m.09ry8b2.
- Bivector sameAs Q663908.
- Bivector sameAs Q663908.
- Bivector sameAs Bivector.
- Bivector wasDerivedFrom Bivector?oldid=597120407.
- Bivector depiction Wedge_product.JPG.
- Bivector isPrimaryTopicOf Bivector.
