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...

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...

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

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...

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...

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...

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...

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

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

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...

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

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

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...

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

The function f(r) can, in principle, be composed of any combination of multivectors. The proof of Cauchy's integral theorem for higher dimensional spaces...

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...

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...

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...

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...