Matches in DBpedia 2016-04 for { <http://dbpedia.org/resource/Cross_product> ?p ?o }
- Cross_product abstract "In mathematics and vector calculus, the cross product or vector product (occasionally directed area product to emphasize the geometric significance) is a binary operation on two vectors in three-dimensional space (R3) and is denoted by the symbol ×. Given two linearly independent vectors a and b, the cross product, a × b, is a vector that is perpendicular to both and therefore normal to the plane containing them. It has many applications in mathematics, physics, engineering, and computer programming. It should not be confused with dot product (projection product).If two vectors have the same direction (or have the exact opposite direction from one another, i.e. are not linearly independent) or if either one has zero length, then their cross product is zero. More generally, the magnitude of the product equals the area of a parallelogram with the vectors for sides; in particular, the magnitude of the product of two perpendicular vectors is the product of their lengths. The cross product is anticommutative (i.e. a × b = −b × a) and is distributive over addition (i.e. a × (b + c) = a × b + a × c). The space R3 together with the cross product is an algebra over the real numbers, which is neither commutative nor associative, but is a Lie algebra with the cross product being the Lie bracket.Like the dot product, it depends on the metric of Euclidean space, but unlike the dot product, it also depends on a choice of orientation or \"handedness\". The product can be generalized in various ways; it can be made independent of orientation by changing the result to pseudovector, or in arbitrary dimensions the exterior product of vectors can be used with a bivector or two-form result. Also, using the orientation and metric structure just as for the traditional 3-dimensional cross product, one can in n dimensions take the product of n − 1 vectors to produce a vector perpendicular to all of them. But if the product is limited to non-trivial binary products with vector results, it exists only in three and seven dimensions. If one adds the further requirement that the product be uniquely defined, then only the 3-dimensional cross product qualifies. (See § Generalizations, below, for other dimensions.)".
- Cross_product thumbnail Cross_product_vector.svg?width=300.
- Cross_product wikiPageExternalLink 1408.5799v1.pdf.
- Cross_product wikiPageExternalLink 117714283.
- Cross_product wikiPageExternalLink dot-and-cross-products.html.
- Cross_product wikiPageExternalLink crosspro.html.
- Cross_product wikiPageExternalLink 0204357.
- Cross_product wikiPageExternalLink historyofmathema027671mbp.
- Cross_product wikiPageExternalLink Cross.pdf.
- Cross_product wikiPageExternalLink RealComplexProducts.shtml.
- Cross_product wikiPageID "157092".
- Cross_product wikiPageLength "66770".
- Cross_product wikiPageOutDegree "243".
- Cross_product wikiPageRevisionID "707021208".
- Cross_product wikiPageWikiLink Aleksandr_Kotelnikov.
- Cross_product wikiPageWikiLink Algebra_over_a_field.
- Cross_product wikiPageWikiLink Angle.
- Cross_product wikiPageWikiLink Angular_momentum.
- Cross_product wikiPageWikiLink Angular_velocity.
- Cross_product wikiPageWikiLink Anticommutativity.
- Cross_product wikiPageWikiLink Antisymmetric_tensor.
- Cross_product wikiPageWikiLink Area.
- Cross_product wikiPageWikiLink Associative_property.
- Cross_product wikiPageWikiLink Augustin-Louis_Cauchy.
- Cross_product wikiPageWikiLink Bilinear_map.
- Cross_product wikiPageWikiLink Binary_operation.
- Cross_product wikiPageWikiLink Binet–Cauchy_identity.
- Cross_product wikiPageWikiLink Bivector.
- Cross_product wikiPageWikiLink Cancellation_property.
- Cross_product wikiPageWikiLink Cartesian_coordinate_system.
- Cross_product wikiPageWikiLink Cartesian_product.
- Cross_product wikiPageWikiLink Category:Analytic_geometry.
- Cross_product wikiPageWikiLink Category:Bilinear_operators.
- Cross_product wikiPageWikiLink Category:Binary_operations.
- Cross_product wikiPageWikiLink Category:Vector_calculus.
- Cross_product wikiPageWikiLink Classical_mechanics.
- Cross_product wikiPageWikiLink Clifford_algebra.
- Cross_product wikiPageWikiLink Collinearity.
- Cross_product wikiPageWikiLink Commutative_property.
- Cross_product wikiPageWikiLink Commutator.
- Cross_product wikiPageWikiLink Composition_algebra.
- Cross_product wikiPageWikiLink Computational_geometry.
- Cross_product wikiPageWikiLink Computer_graphics.
- Cross_product wikiPageWikiLink Computer_programming.
- Cross_product wikiPageWikiLink Connecticut.
- Cross_product wikiPageWikiLink Cross_product.
- Cross_product wikiPageWikiLink Curl_(mathematics).
- Cross_product wikiPageWikiLink Determinant.
- Cross_product wikiPageWikiLink Distributive_property.
- Cross_product wikiPageWikiLink Dot_product.
- Cross_product wikiPageWikiLink Dual_space.
- Cross_product wikiPageWikiLink Edward_Arthur_Milne.
- Cross_product wikiPageWikiLink Edwin_Bidwell_Wilson.
- Cross_product wikiPageWikiLink Einstein_notation.
- Cross_product wikiPageWikiLink Elements_of_Dynamic.
- Cross_product wikiPageWikiLink Engineering.
- Cross_product wikiPageWikiLink Epipolar_geometry.
- Cross_product wikiPageWikiLink Euclidean_space.
- Cross_product wikiPageWikiLink Euclidean_vector.
- Cross_product wikiPageWikiLink Exterior_algebra.
- Cross_product wikiPageWikiLink Formal_calculation.
- Cross_product wikiPageWikiLink Geometric_algebra.
- Cross_product wikiPageWikiLink Gradient.
- Cross_product wikiPageWikiLink Gramian_matrix.
- Cross_product wikiPageWikiLink Handedness.
- Cross_product wikiPageWikiLink Heisenberg_group.
- Cross_product wikiPageWikiLink Hermann_Grassmann.
- Cross_product wikiPageWikiLink Hodge_dual.
- Cross_product wikiPageWikiLink Hurwitzs_theorem_(composition_algebras).
- Cross_product wikiPageWikiLink Indexed_family.
- Cross_product wikiPageWikiLink Inner_product_space.
- Cross_product wikiPageWikiLink Invertible_matrix.
- Cross_product wikiPageWikiLink Isotropy.
- Cross_product wikiPageWikiLink Jacobi_identity.
- Cross_product wikiPageWikiLink James_Clerk_Maxwell.
- Cross_product wikiPageWikiLink Java_(programming_language).
- Cross_product wikiPageWikiLink Joseph-Louis_Lagrange.
- Cross_product wikiPageWikiLink Josiah_Willard_Gibbs.
- Cross_product wikiPageWikiLink Kernel_(linear_algebra).
- Cross_product wikiPageWikiLink Lagranges_identity.
- Cross_product wikiPageWikiLink Laplace_expansion.
- Cross_product wikiPageWikiLink Levi-Civita_symbol.
- Cross_product wikiPageWikiLink Lie_algebra.
- Cross_product wikiPageWikiLink Lie_theory.
- Cross_product wikiPageWikiLink Linearity.
- Cross_product wikiPageWikiLink Lorentz_force.
- Cross_product wikiPageWikiLink Main_diagonal.
- Cross_product wikiPageWikiLink Mathematics.
- Cross_product wikiPageWikiLink Matrix_(mathematics).
- Cross_product wikiPageWikiLink Maxwells_equations.
- Cross_product wikiPageWikiLink Methuen_Publishing.
- Cross_product wikiPageWikiLink Metric_space.
- Cross_product wikiPageWikiLink Mixed_tensor.
- Cross_product wikiPageWikiLink Mnemonic.
- Cross_product wikiPageWikiLink Moment_(physics).
- Cross_product wikiPageWikiLink Multilinear_algebra.
- Cross_product wikiPageWikiLink Multiplication_sign.
- Cross_product wikiPageWikiLink Multivector.
- Cross_product wikiPageWikiLink Norm_(mathematics).
- Cross_product wikiPageWikiLink Normal_(geometry).