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...

to a general multivector, called the multivector derivative. Let F {\displaystyle F} be a multivector-valued function of a multivector. The directional...

Multiplication of vectors results in higher-dimensional objects called multivectors. Compared to other formalisms for manipulating geometric objects, geometric...

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...

In differential geometry, a field in mathematics, a multivector field, polyvector field of degree k {\displaystyle k} , or k {\displaystyle k} -vector...

respect to each argument. It involves concepts such as matrices, tensors, multivectors, systems of linear equations, higher-dimensional spaces, determinants...

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...

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...

between vector spaces is a natural extension of the map to arbitrary multivectors. It is the unique unital algebra homomorphism of exterior algebras whose...

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...

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...

in three dimensions E.g. Riemann curvature tensor 2 Inverse metric tensor, bivector, e.g., Poisson structure E.g. elasticity tensor ⋮ N Multivector ⋮...

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...

Fiber bundle Geodesic Levi-Civita connection Linear map Manifold Matrix Multivector Pseudotensor Spinor Vector Vector space Notable tensors Mathematicians...

generalized to the notions of projection and rejection of a general multivector onto/from any invertible k-blade. Scalar projection Vector notation Perwass...

Fiber bundle Geodesic Levi-Civita connection Linear map Manifold Matrix Multivector Pseudotensor Spinor Vector Vector space Notable tensors Mathematicians...

syndrome, a rare liver disorder Rotor (mathematics), an even-graded multivector used to produce rotations and some other affine transformations Curl...

Fiber bundle Geodesic Levi-Civita connection Linear map Manifold Matrix Multivector Pseudotensor Spinor Vector Vector space Notable tensors Mathematicians...

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...

Fiber bundle Geodesic Levi-Civita connection Linear map Manifold Matrix Multivector Pseudotensor Spinor Vector Vector space Notable tensors Mathematicians...

mathematics and physics (Kluwer: Dordrecht/Boston, 1984). D. Hestenes, Multivector Calculus, Journal of Mathematical Analysis and Applications 24: 313–325...

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...

Fiber bundle Geodesic Levi-Civita connection Linear map Manifold Matrix Multivector Pseudotensor Spinor Vector Vector space Notable tensors Mathematicians...

Fiber bundle Geodesic Levi-Civita connection Linear map Manifold Matrix Multivector Pseudotensor Spinor Vector Vector space Notable tensors Mathematicians...

Fiber bundle Geodesic Levi-Civita connection Linear map Manifold Matrix Multivector Pseudotensor Spinor Vector Vector space Notable tensors Mathematicians...

Jacobian determinant of a change-of-coordinate function. Grassmannian Multivector Exterior algebra Differential form Geometric algebra Clifford algebra...

Fiber bundle Geodesic Levi-Civita connection Linear map Manifold Matrix Multivector Pseudotensor Spinor Vector Vector space Notable tensors Mathematicians...

products of vectors and then reversing the order of each product.: 13  For multivector A {\textstyle A} arising from a product of vectors, a 1 a 2 … a r − 1...

Fiber bundle Geodesic Levi-Civita connection Linear map Manifold Matrix Multivector Pseudotensor Spinor Vector Vector space Notable tensors Mathematicians...

Fiber bundle Geodesic Levi-Civita connection Linear map Manifold Matrix Multivector Pseudotensor Spinor Vector Vector space Notable tensors Mathematicians...