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Element of an exterior algebra
In multilinear algebra, a multivector, sometimes called Clifford number or multor, is an element of the exterior algebra Λ(V) of a vector space V. This
Multivector
Infinitesimal calculus on functions defined on a geometric algebra
to a general multivector, called the multivector derivative. Let F {\displaystyle F} be a multivector-valued function of a multivector. The directional
Geometric_calculus
Algebraic structure designed for geometry
Multiplication of vectors results in higher-dimensional objects called multivectors. Compared to other formalisms for manipulating geometric objects, geometric
Geometric_algebra
In differential geometry, a field in mathematics, a multivector field, polyvector field of degree k {\displaystyle k} , or k {\displaystyle k} -vector
Polyvector_field
Object in geometric algebra
Cleven(V) consisting of multivectors R such that R R ~ = 1. {\displaystyle R{\tilde {R}}=1.} That is, it consists of multivectors that can be written as
Rotor_(mathematics)
as the Schouten bracket, is a type of graded Lie bracket defined on multivector fields on a smooth manifold extending the Lie bracket of vector fields
Schouten–Nijenhuis_bracket
Branch of mathematics
respect to each argument. It involves concepts such as matrices, tensors, multivectors, systems of linear equations, higher-dimensional spaces, determinants
Multilinear_algebra
Algebraic object with geometric applications
in three dimensions e.g. Riemann curvature tensor 2 bivector, e.g. Poisson structure, inverse metric tensor e.g. elasticity tensor ⋮ N multivector ⋮
Tensor
Exterior algebraic map taking tensors from p forms to n-p forms
G b {\displaystyle a^{\mathrm {T} }Gb} , where a and b are arbitrary multivectors represented by 2 n × 1 {\displaystyle 2^{n}\times 1} column matrices
Hodge_star_operator
Mapping from p forms to p-1 forms
a vector X (which has grade 1), a homogeneous multivector a having grade p, and an arbitrary multivector b, the right interior product satisfies the rule
Interior_product
Topics referred to by the same term
and physics, k-vector may refer to: A wave vector k Crystal momentum A multivector of grade k, also called a k-vector, the dual of a differential k-form
K-vector
Algebra associated to any vector space
while a more general sum of blades of arbitrary degree is called a multivector. The linear span of the k {\displaystyle k} -blades is called the k {\displaystyle
Exterior_algebra
Broad concept generalizing scalars in mathematics and physics
historical reasons. Vector quaternion, a quaternion with a zero real part Multivector or p-vector, an element of the exterior algebra of a vector space. Spinors
Vector (mathematics and physics)
Vector_(mathematics_and_physics)
Algebraic operation on coordinate vectors
Fiber bundle Geodesic Levi-Civita connection Linear map Manifold Matrix Multivector Pseudotensor Spinor Vector Vector space Notable tensors Mathematics Kronecker
Dot_product
Concept in linear algebra
generalized to the notions of projection and rejection of a general multivector onto/from any invertible k-blade. Scalar projection Vector notation Perwass
Vector_projection
Mathematical operation on vectors in 3D space
product could be generalised to arbitrary multivectors in three dimensions, which results in a multivector consisting of only elements of grades 1 (1-vectors/true
Cross_product
Theory of gravitation as curved spacetime
Fiber bundle Geodesic Levi-Civita connection Linear map Manifold Matrix Multivector Pseudotensor Spinor Vector Vector space Notable tensors Mathematics Kronecker
General_relativity
Theory of interwoven space and time by Albert Einstein
Fiber bundle Geodesic Levi-Civita connection Linear map Manifold Matrix Multivector Pseudotensor Spinor Vector Vector space Notable tensors Mathematics Kronecker
Special_relativity
Array of numbers
Fiber bundle Geodesic Levi-Civita connection Linear map Manifold Matrix Multivector Pseudotensor Spinor Vector Vector space Notable tensors Mathematics Kronecker
Matrix_(mathematics)
Mathematical function, in linear algebra
Fiber bundle Geodesic Levi-Civita connection Linear map Manifold Matrix Multivector Pseudotensor Spinor Vector Vector space Notable tensors Mathematics Kronecker
Linear_map
Shorthand notation for tensor operations
Fiber bundle Geodesic Levi-Civita connection Linear map Manifold Matrix Multivector Pseudotensor Spinor Vector Vector space Notable tensors Mathematics Kronecker
Einstein_notation
Branch of physics which studies the behavior of materials modeled as continuous media
Fiber bundle Geodesic Levi-Civita connection Linear map Manifold Matrix Multivector Pseudotensor Spinor Vector Vector space Notable tensors Mathematics Kronecker
Continuum_mechanics
Property of a mathematical space
Fiber bundle Geodesic Levi-Civita connection Linear map Manifold Matrix Multivector Pseudotensor Spinor Vector Vector space Notable tensors Mathematics Kronecker
Dimension
Matrix operation which flips a matrix over its diagonal
Fiber bundle Geodesic Levi-Civita connection Linear map Manifold Matrix Multivector Pseudotensor Spinor Vector Vector space Notable tensors Mathematics Kronecker
Transpose
Straight path on a curved surface or a Riemannian manifold
Fiber bundle Geodesic Levi-Civita connection Linear map Manifold Matrix Multivector Pseudotensor Spinor Vector Vector space Notable tensors Mathematics Kronecker
Geodesic
Physical quantity that changes sign with improper rotation
terminology to describe the various combinations is provided. For example, a multivector is a summation of k-fold wedge products of various k-values. A k-fold
Pseudovector
Topological space that locally resembles Euclidean space
Fiber bundle Geodesic Levi-Civita connection Linear map Manifold Matrix Multivector Pseudotensor Spinor Vector Vector space Notable tensors Mathematics Kronecker
Manifold
economic ambitions. At the heart of its international diplomacy is a multivector foreign policy, which aims to maintain balanced and diverse relations
Foreign relations of Kazakhstan
Foreign_relations_of_Kazakhstan
Conserved physical quantity; rotational analogue of linear momentum
Fiber bundle Geodesic Levi-Civita connection Linear map Manifold Matrix Multivector Pseudotensor Spinor Vector Vector space Notable tensors Mathematics Kronecker
Angular_momentum
Setting of relativistic physics in geometric algebra
products of vectors and then reversing the order of each product. For multivector A {\textstyle A} arising from a product of vectors, a 1 a 2 … a r − 1
Spacetime_algebra
Branch of mathematics
Fiber bundle Geodesic Levi-Civita connection Linear map Manifold Matrix Multivector Pseudotensor Spinor Vector Vector space Notable tensors Mathematics Kronecker
Differential_geometry
Four-dimensional number system
{\displaystyle \operatorname {Cl} _{3,0}(\mathbb {R} ).} This is an associative multivector algebra built up from fundamental basis elements σ1, σ2, σ3 using the
Quaternion
Topics referred to by the same term
syndrome, a rare liver disorder Rotor (mathematics), an even-graded multivector used to produce rotations and some other affine transformations Curl
Rotor
American physicist and science educator
mathematics and physics (Kluwer: Dordrecht/Boston, 1984). D. Hestenes, Multivector Calculus, Journal of Mathematical Analysis and Applications 24: 313–325
David_Hestenes
Expression that may be integrated over a region
Fiber bundle Geodesic Levi-Civita connection Linear map Manifold Matrix Multivector Pseudotensor Spinor Vector Vector space Notable tensors Mathematics Kronecker
Differential_form
Type of derivative in differential geometry
Fiber bundle Geodesic Levi-Civita connection Linear map Manifold Matrix Multivector Pseudotensor Spinor Vector Vector space Notable tensors Mathematics Kronecker
Lie_derivative
Set of vectors used to define coordinates
Fiber bundle Geodesic Levi-Civita connection Linear map Manifold Matrix Multivector Pseudotensor Spinor Vector Vector space Notable tensors Mathematics Kronecker
Basis_(linear_algebra)
Specification of a derivative along a tangent vector of a manifold
Fiber bundle Geodesic Levi-Civita connection Linear map Manifold Matrix Multivector Pseudotensor Spinor Vector Vector space Notable tensors Mathematics Kronecker
Covariant_derivative
Mathematical operation on vector spaces
Fiber bundle Geodesic Levi-Civita connection Linear map Manifold Matrix Multivector Pseudotensor Spinor Vector Vector space Notable tensors Mathematics Kronecker
Tensor_product
Vector behavior under coordinate changes
Fiber bundle Geodesic Levi-Civita connection Linear map Manifold Matrix Multivector Pseudotensor Spinor Vector Vector space Notable tensors Mathematics Kronecker
Covariance and contravariance of vectors
Covariance_and_contravariance_of_vectors
1989–1991 mass movement in Ukraine
Liberation Revolution in Ukraine as a product of a social movement and multivector network of structures]. Kharkiv National University of Internal Affairs
1989–1991 Ukrainian revolution
1989–1991_Ukrainian_revolution
Provides integral formulas for all derivatives of a holomorphic function
{\displaystyle f(r)} can, in principle, be composed of any combination of multivectors. The proof of Cauchy's integral theorem for higher dimensional spaces
Cauchy's_integral_formula
Mathematical function of two variables; outputs 1 if they are equal, 0 otherwise
Fiber bundle Geodesic Levi-Civita connection Linear map Manifold Matrix Multivector Pseudotensor Spinor Vector Vector space Notable tensors Mathematics Kronecker
Kronecker_delta
Non-tensorial representation of the spin group
Fiber bundle Geodesic Levi-Civita connection Linear map Manifold Matrix Multivector Pseudotensor Spinor Vector Vector space Notable tensors Mathematics Kronecker
Spinor
Method for specifying point positions
Fiber bundle Geodesic Levi-Civita connection Linear map Manifold Matrix Multivector Pseudotensor Spinor Vector Vector space Notable tensors Mathematics Kronecker
Coordinate_system
extension of linear algebra building upon concepts of p-vectors and multivectors with Grassmann algebra. Multiplicative number theory a subfield of analytic
Glossary of areas of mathematics
Glossary_of_areas_of_mathematics
Tensor in differential geometry
Fiber bundle Geodesic Levi-Civita connection Linear map Manifold Matrix Multivector Pseudotensor Spinor Vector Vector space Notable tensors Mathematics Kronecker
Ricci_curvature
finite-dimensional geometric algebras (GA). The elements of UGA are called multivectors. Every multivector can be written as the sum of several r-vectors. Some r-vectors
Universal_geometric_algebra
Mathematical object that describes the electromagnetic field in spacetime
Fiber bundle Geodesic Levi-Civita connection Linear map Manifold Matrix Multivector Pseudotensor Spinor Vector Vector space Notable tensors Mathematics Kronecker
Electromagnetic_tensor
Structure defining distance on a manifold
Fiber bundle Geodesic Levi-Civita connection Linear map Manifold Matrix Multivector Pseudotensor Spinor Vector Vector space Notable tensors Mathematics Kronecker
Metric_tensor
Continuous surjection satisfying a local triviality condition
Fiber bundle Geodesic Levi-Civita connection Linear map Manifold Matrix Multivector Pseudotensor Spinor Vector Vector space Notable tensors Mathematics Kronecker
Fiber_bundle
Unital algebra homomorphism of exterior algebras
between vector spaces is a natural extension of the map to arbitrary multivectors. It is the unique unital algebra homomorphism of exterior algebras whose
Outermorphism
Study of curves from a differential point of view
Fiber bundle Geodesic Levi-Civita connection Linear map Manifold Matrix Multivector Pseudotensor Spinor Vector Vector space Notable tensors Mathematics Kronecker
Differentiable_curve
Bilateral relations
relationship, however, is limited by historical memory and Vietnam's multivector foreign policy. While fears about regime change have lowered, the U.S
United States–Vietnam relations
United_States–Vietnam_relations
Tensor describing energy momentum density in spacetime
Fiber bundle Geodesic Levi-Civita connection Linear map Manifold Matrix Multivector Pseudotensor Spinor Vector Vector space Notable tensors Mathematics Kronecker
Stress–energy_tensor
Operation in mathematics
Fiber bundle Geodesic Levi-Civita connection Linear map Manifold Matrix Multivector Pseudotensor Spinor Vector Vector space Notable tensors Mathematics Kronecker
Tensor_contraction
Abbreviation in the fields of special and general relativity
Fiber bundle Geodesic Levi-Civita connection Linear map Manifold Matrix Multivector Pseudotensor Spinor Vector Vector space Notable tensors Mathematics Kronecker
Four-tensor
Algebra of 4D spacetime
conjugation. If g ∈ G 3 {\displaystyle g\in \mathbb {G} _{3}} is an arbitrary multivector and ⟨ g ⟩ j {\displaystyle \langle g\rangle _{j}} projects g {\displaystyle
Algebra_of_physical_space
Universal construction in multilinear algebra
Fiber bundle Geodesic Levi-Civita connection Linear map Manifold Matrix Multivector Pseudotensor Spinor Vector Vector space Notable tensors Mathematics Kronecker
Tensor_algebra
Assignment of a tensor continuously varying across a region of space
Fiber bundle Geodesic Levi-Civita connection Linear map Manifold Matrix Multivector Pseudotensor Spinor Vector Vector space Notable tensors Mathematics Kronecker
Tensor_field
Index of articles associated with the same name
scalar plus a bivector. The geometric product is well defined for any multivectors as arguments. A bilinear product in an algebra over a field. A Lie bracket
Vector_multiplication
Scalar measure of the rotational inertia with respect to a fixed axis of rotation
Fiber bundle Geodesic Levi-Civita connection Linear map Manifold Matrix Multivector Pseudotensor Spinor Vector Vector space Notable tensors Mathematics Kronecker
Moment_of_inertia
Antisymmetric permutation object acting on tensors
Fiber bundle Geodesic Levi-Civita connection Linear map Manifold Matrix Multivector Pseudotensor Spinor Vector Vector space Notable tensors Mathematics Kronecker
Levi-Civita_symbol
Society becoming more democratic
Liberation Revolution in Ukraine as a product of a social movement and multivector network of structures]. Kharkiv National University of Internal Affairs
Democratization
Coordinate-free definition of a tensor
Fiber bundle Geodesic Levi-Civita connection Linear map Manifold Matrix Multivector Pseudotensor Spinor Vector Vector space Notable tensors Mathematics Kronecker
Tensor_(intrinsic_definition)
Object in differential geometry
Fiber bundle Geodesic Levi-Civita connection Linear map Manifold Matrix Multivector Pseudotensor Spinor Vector Vector space Notable tensors Mathematics Kronecker
Torsion_tensor
Element of a unital algebra over the field of real numbers
\\0&i\not =j.\end{cases}}} Imposing closure under multiplication generates a multivector space spanned by a basis of 2 k {\displaystyle 2^{k}} elements, { 1
Hypercomplex_number
Tensor field in Riemannian geometry
Fiber bundle Geodesic Levi-Civita connection Linear map Manifold Matrix Multivector Pseudotensor Spinor Vector Vector space Notable tensors Mathematics Kronecker
Riemann_curvature_tensor
Topics referred to by the same term
differential form with a vector field Left contraction and right contraction of multivectors in a geometric algebra, extensions of the inner product One of the rules
Contraction
Mathematical Concept
Fiber bundle Geodesic Levi-Civita connection Linear map Manifold Matrix Multivector Pseudotensor Spinor Vector Vector space Notable tensors Mathematics Kronecker
Voigt_notation
Array of numbers describing a metric connection
Fiber bundle Geodesic Levi-Civita connection Linear map Manifold Matrix Multivector Pseudotensor Spinor Vector Vector space Notable tensors Mathematics Kronecker
Christoffel_symbols
Tensor index notation for tensor-based calculations
Fiber bundle Geodesic Levi-Civita connection Linear map Manifold Matrix Multivector Pseudotensor Spinor Vector Vector space Notable tensors Mathematics Kronecker
Ricci_calculus
Isomorphism between the tangent and cotangent bundles of a manifold
Fiber bundle Geodesic Levi-Civita connection Linear map Manifold Matrix Multivector Pseudotensor Spinor Vector Vector space Notable tensors Mathematics Kronecker
Musical_isomorphism
Ternary operation on vectors
ISBN 0-521-00551-5. Janne Pesonen. "Geometric Algebra of One and Many Multivector Variables" (PDF). p. 37. "Permutation Tensor". Wolfram. Retrieved 21
Triple_product
Differential form of degree one or section of a cotangent bundle
Fiber bundle Geodesic Levi-Civita connection Linear map Manifold Matrix Multivector Pseudotensor Spinor Vector Vector space Notable tensors Mathematics Kronecker
One-form
Quaternion of norm 1 (unit quaternion)
{\displaystyle {\mathcal {G}}(3,0)} . In a departure from Hamilton's definition, multivector versors are not required to have unit norm, just to be invertible. Normalisation
Versor
Second order tensor in vector algebra
and polyadic. Kronecker product Bivector Polyadic algebra Unit vector Multivector Differential form Quaternions Field (mathematics) The cross product only
Dyadics
Operation on differential forms
Fiber bundle Geodesic Levi-Civita connection Linear map Manifold Matrix Multivector Pseudotensor Spinor Vector Vector space Notable tensors Mathematics Kronecker
Exterior_derivative
Mathematical notation
Fiber bundle Geodesic Levi-Civita connection Linear map Manifold Matrix Multivector Pseudotensor Spinor Vector Vector space Notable tensors Mathematics Kronecker
Multi-index_notation
Measure of the curvature of a pseudo-Riemannian manifold
Fiber bundle Geodesic Levi-Civita connection Linear map Manifold Matrix Multivector Pseudotensor Spinor Vector Vector space Notable tensors Mathematics Kronecker
Weyl_tensor
differential forms on a Poisson manifold form a Gerstenhaber algebra. The multivector fields on a manifold form a Gerstenhaber algebra using the Schouten–Nijenhuis
Gerstenhaber_algebra
Sum of a scalar and vector in Clifford algebra
defined as the inversion of the sign of odd-grade multivectors, while maintaining the even-grade multivectors invariant: Four special subspaces can be defined
Paravector
Tensor invariant under permutations of vectors it acts on
Fiber bundle Geodesic Levi-Civita connection Linear map Manifold Matrix Multivector Pseudotensor Spinor Vector Vector space Notable tensors Mathematics Kronecker
Symmetric_tensor
Affine connection on the tangent bundle of a manifold
Fiber bundle Geodesic Levi-Civita connection Linear map Manifold Matrix Multivector Pseudotensor Spinor Vector Vector space Notable tensors Mathematics Kronecker
Levi-Civita_connection
Operation that pairs a left and a right R-module into an abelian group
Fiber bundle Geodesic Levi-Civita connection Linear map Manifold Matrix Multivector Pseudotensor Spinor Vector Vector space Notable tensors Mathematics Kronecker
Tensor_product_of_modules
Representation of mechanical stress at every point within a deformed 3D object
Fiber bundle Geodesic Levi-Civita connection Linear map Manifold Matrix Multivector Pseudotensor Spinor Vector Vector space Notable tensors Mathematics Kronecker
Cauchy_stress_tensor
Decomposition in multilinear algebra
Fiber bundle Geodesic Levi-Civita connection Linear map Manifold Matrix Multivector Pseudotensor Spinor Vector Vector space Notable tensors Mathematics Kronecker
Tensor_rank_decomposition
Tensor that describes the 4D geometry of spacetime
Fiber bundle Geodesic Levi-Civita connection Linear map Manifold Matrix Multivector Pseudotensor Spinor Vector Vector space Notable tensors Mathematics Kronecker
Metric tensor (general relativity)
Metric_tensor_(general_relativity)
Formulations of electromagnetism
0}(\mathbb {R} )} , the field and current are represented by multivectors. The field multivector, known as the Riemann–Silberstein vector, is F = E + I c
Mathematical descriptions of the electromagnetic field
Mathematical_descriptions_of_the_electromagnetic_field
Ways of writing certain laws of physics
Fiber bundle Geodesic Levi-Civita connection Linear map Manifold Matrix Multivector Pseudotensor Spinor Vector Vector space Notable tensors Mathematics Kronecker
Covariant formulation of classical electromagnetism
Covariant_formulation_of_classical_electromagnetism
Construct in differenital geometry
Fiber bundle Geodesic Levi-Civita connection Linear map Manifold Matrix Multivector Pseudotensor Spinor Vector Vector space Notable tensors Mathematics Kronecker
Metric_connection
Ways to represent 3D rotations
expected. This rotation formula is valid not only for vectors but for any multivector. In addition, when Euler angles are used, the complexity of the operation
Rotation formulations in three dimensions
Rotation_formulations_in_three_dimensions
Differential form
Fiber bundle Geodesic Levi-Civita connection Linear map Manifold Matrix Multivector Pseudotensor Spinor Vector Vector space Notable tensors Mathematics Kronecker
Volume_form
Topics referred to by the same term
Schouten–Nijenhuis bracket (2 versions, defined on either symmetric or antisymmetric multivectors) This disambiguation page lists articles associated with the title Nijenhuis
Nijenhuis_bracket
Function that is invariant under all permutations of its variables
Fiber bundle Geodesic Levi-Civita connection Linear map Manifold Matrix Multivector Pseudotensor Spinor Vector Vector space Notable tensors Mathematics Kronecker
Symmetric_function
Fiber bundle Geodesic Levi-Civita connection Linear map Manifold Matrix Multivector Pseudotensor Spinor Vector Vector space Notable tensors Mathematics Kronecker
Symmetrization
System of moving vectors in differential geometry
Fiber bundle Geodesic Levi-Civita connection Linear map Manifold Matrix Multivector Pseudotensor Spinor Vector Vector space Notable tensors Mathematics Kronecker
Parallel_transport
Tensor used in general relativity
Fiber bundle Geodesic Levi-Civita connection Linear map Manifold Matrix Multivector Pseudotensor Spinor Vector Vector space Notable tensors Mathematics Kronecker
Einstein_tensor
Tensor operator generalizes the notion of operators which are scalars and vectors
Fiber bundle Geodesic Levi-Civita connection Linear map Manifold Matrix Multivector Pseudotensor Spinor Vector Vector space Notable tensors Mathematics Kronecker
Tensor_operator
Math/physics concept
Fiber bundle Geodesic Levi-Civita connection Linear map Manifold Matrix Multivector Pseudotensor Spinor Vector Vector space Notable tensors Mathematics Kronecker
Connection_form
MULTIVECTOR
MULTIVECTOR
MULTIVECTOR
MULTIVECTOR
Boy/Male
English American
From the beaver meadow.
Boy/Male
Indian
Princely Lord God of heaven
Male
Greek
(ΠεÏσεÏÏ‚) Greek myth name of the founder of Mycenae and the hero who killed the half-mortal gorgon Medousa. If Greek, the first element of the name might have derived from the word pertho, PERSEUS means "to sack, to destroy." And according to Carl Daling Buck in his Comparative Grammar of Greek and Latin, the -eus suffix found in so many Greek names is typically used to form an agent noun. If so, Perseus was a "destroyer" by profession, i.e. a "soldier," which is a fitting name for this legendary hero.Â
Girl/Female
Hindu
Flame, Light, Lamp, The light of the Sun
Boy/Male
Tamil
Chaaruchithra | சாரà¯à®šà®¿à®¤à¯à®°
One of the kauravas
Surname or Lastname
English (West Midlands)
English (West Midlands) : topographic name from West Midland Middle English rugge, a variant of rigge ‘ridge’, or a habitational name from the village of Rudge in Shropshire, which is named with this word.English (West Midlands) : from a medieval personal name, a pet form of Roger.English (West Midlands) : nickname for a person with red hair or a ruddy complexion, from Old French r(o)uge ‘red’ (Latin rubeus).
Surname or Lastname
English
English : occupational name for a maker or seller of goblets, from Old French hanapier.German and Dutch : from the Germanic personal name Hambert, composed of either haim, heim ‘home’ or hagan ‘enclosure’, ‘protected place’ + berht ‘bright’, ‘famous’.
Girl/Female
Indian
Desired
Girl/Female
Assamese, Indian
Name of Lord Shiva
Boy/Male
Hindu
Vinashana destroyer of enemys valour
MULTIVECTOR
MULTIVECTOR
MULTIVECTOR
MULTIVECTOR
MULTIVECTOR