Matches in DBpedia 2016-04 for { <http://dbpedia.org/resource/Bivector> ?p ?o }
- 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.".
- 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 wikiPageLength "63342".
- Bivector wikiPageOutDegree "188".
- Bivector wikiPageRevisionID "700143474".
- Bivector wikiPageWikiLink Alternatization.
- Bivector wikiPageWikiLink Angle.
- Bivector wikiPageWikiLink Angle_of_rotation.
- Bivector wikiPageWikiLink Angular_momentum.
- Bivector wikiPageWikiLink Angular_velocity.
- Bivector wikiPageWikiLink Anticommutativity.
- Bivector wikiPageWikiLink Antisymmetric_relation.
- Bivector wikiPageWikiLink Area.
- Bivector wikiPageWikiLink Associative_property.
- Bivector wikiPageWikiLink Axis–angle_representation.
- Bivector wikiPageWikiLink Basis_(linear_algebra).
- Bivector wikiPageWikiLink Blade_(geometry).
- Bivector wikiPageWikiLink Cambridge_University_Press.
- Bivector wikiPageWikiLink Cartesian_coordinate_system.
- Bivector wikiPageWikiLink Category:Clifford_algebras.
- Bivector wikiPageWikiLink Category:Geometric_algebra.
- Bivector wikiPageWikiLink Category:Multilinear_algebra.
- Bivector wikiPageWikiLink Category:Tensors.
- Bivector wikiPageWikiLink Category:Vector_calculus.
- Bivector wikiPageWikiLink Characteristic_polynomial.
- Bivector wikiPageWikiLink Charge_density.
- Bivector wikiPageWikiLink Classification_of_Clifford_algebras.
- Bivector wikiPageWikiLink Clifford_algebra.
- Bivector wikiPageWikiLink Clockwise.
- Bivector wikiPageWikiLink Commutative_property.
- Bivector wikiPageWikiLink Commutator.
- Bivector wikiPageWikiLink Complex_number.
- Bivector wikiPageWikiLink Covering_group.
- Bivector wikiPageWikiLink Cross_product.
- Bivector wikiPageWikiLink Curl_(mathematics).
- Bivector wikiPageWikiLink Current_density.
- Bivector wikiPageWikiLink David_Hestenes.
- Bivector wikiPageWikiLink Degeneracy_(mathematics).
- Bivector wikiPageWikiLink Del.
- Bivector wikiPageWikiLink Determinant.
- Bivector wikiPageWikiLink Differential_operator.
- Bivector wikiPageWikiLink Distributive_property.
- Bivector wikiPageWikiLink Divergence.
- Bivector wikiPageWikiLink Dot_product.
- Bivector wikiPageWikiLink Edwin_Bidwell_Wilson.
- Bivector wikiPageWikiLink Eigenvalues_and_eigenvectors.
- Bivector wikiPageWikiLink Electric_field.
- Bivector wikiPageWikiLink Electromagnetic_four-potential.
- Bivector wikiPageWikiLink Electromagnetic_tensor.
- Bivector wikiPageWikiLink Euclidean_distance.
- Bivector wikiPageWikiLink Euclidean_space.
- Bivector wikiPageWikiLink Euclidean_vector.
- Bivector wikiPageWikiLink Eulers_formula.
- Bivector wikiPageWikiLink Exponential_function.
- Bivector wikiPageWikiLink Exterior_algebra.
- Bivector wikiPageWikiLink File:Tesseract.gif.
- Bivector wikiPageWikiLink Five-dimensional_space.
- Bivector wikiPageWikiLink Force.
- Bivector wikiPageWikiLink Four-current.
- Bivector wikiPageWikiLink Fundamental_theorem_of_algebra.
- Bivector wikiPageWikiLink Geometric_algebra.
- Bivector wikiPageWikiLink Gradient.
- Bivector wikiPageWikiLink Hermann_Grassmann.
- Bivector wikiPageWikiLink Hodge_dual.
- Bivector wikiPageWikiLink Imaginary_unit.
- Bivector wikiPageWikiLink Isomorphism.
- Bivector wikiPageWikiLink Josiah_Willard_Gibbs.
- Bivector wikiPageWikiLink Law_of_cosines.
- Bivector wikiPageWikiLink Lie_algebra.
- Bivector wikiPageWikiLink Line_segment.
- Bivector wikiPageWikiLink Linear_subspace.
- Bivector wikiPageWikiLink Lorentz_group.
- Bivector wikiPageWikiLink Lorentz_transformation.
- Bivector wikiPageWikiLink Magnetic_field.
- Bivector wikiPageWikiLink Magnitude_(mathematics).
- Bivector wikiPageWikiLink Mathematics.
- Bivector wikiPageWikiLink Maxwells_equations.
- Bivector wikiPageWikiLink Metric_signature.
- Bivector wikiPageWikiLink Metric_tensor.
- Bivector wikiPageWikiLink Minkowski_space.
- Bivector wikiPageWikiLink Momentum.
- Bivector wikiPageWikiLink Multilinear_algebra.
- Bivector wikiPageWikiLink Multivector.
- Bivector wikiPageWikiLink Norm_(mathematics).
- Bivector wikiPageWikiLink Normal_(geometry).
- Bivector wikiPageWikiLink Oliver_Heaviside.
- Bivector wikiPageWikiLink Orientation_(geometry).
- Bivector wikiPageWikiLink Orthogonal_complement.
- Bivector wikiPageWikiLink Orthogonal_matrix.
- Bivector wikiPageWikiLink Orthonormality.
- Bivector wikiPageWikiLink Parallelogram.
- Bivector wikiPageWikiLink Physics.
- Bivector wikiPageWikiLink Plane_(geometry).
- Bivector wikiPageWikiLink Plane_of_rotation.
- Bivector wikiPageWikiLink Positive_definiteness.
- Bivector wikiPageWikiLink Princeton_University_Press.