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...
33 KB (4,882 words) - 23:37, 14 March 2025
Geometric calculus (redirect from Multivector derivative)
to a general multivector, called the multivector derivative. Let F {\displaystyle F} be a multivector-valued function of a multivector. The directional...
16 KB (3,338 words) - 21:48, 12 August 2024
Multiplication of vectors results in higher-dimensional objects called multivectors. Compared to other formalisms for manipulating geometric objects, geometric...
93 KB (13,801 words) - 22:00, 13 April 2025
Polyvector field (redirect from Multivector field)
In differential geometry, a field in mathematics, a multivector field, polyvector field of degree k {\displaystyle k} , or k {\displaystyle k} -vector...
4 KB (698 words) - 17:43, 18 August 2024
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...
7 KB (839 words) - 07:52, 8 March 2024
respect to each argument. It involves concepts such as matrices, tensors, multivectors, systems of linear equations, higher-dimensional spaces, determinants...
6 KB (661 words) - 02:59, 5 March 2024
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...
7 KB (1,153 words) - 18:01, 18 August 2024
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...
77 KB (12,118 words) - 20:04, 2 May 2025
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...
382 bytes (88 words) - 10:49, 1 December 2018
Fiber bundle Geodesic Levi-Civita connection Linear map Manifold Matrix Multivector Pseudotensor Spinor Vector Vector space Notable tensors Mathematicians...
20 KB (2,550 words) - 21:08, 14 April 2025
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...
10 KB (2,684 words) - 04:26, 1 June 2025
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...
33 KB (4,332 words) - 18:33, 11 May 2025
Fiber bundle Geodesic Levi-Civita connection Linear map Manifold Matrix Multivector Pseudotensor Spinor Vector Vector space Notable tensors Mathematicians...
14 KB (2,074 words) - 15:45, 7 February 2025
in three dimensions E.g. Riemann curvature tensor 2 Inverse metric tensor, bivector, e.g., Poisson structure E.g. elasticity tensor ⋮ N Multivector ⋮...
69 KB (9,357 words) - 21:16, 23 May 2025
generalized to the notions of projection and rejection of a general multivector onto/from any invertible k-blade. Scalar projection Vector notation Perwass...
13 KB (1,718 words) - 13:42, 8 May 2025
Fiber bundle Geodesic Levi-Civita connection Linear map Manifold Matrix Multivector Pseudotensor Spinor Vector Vector space Notable tensors Mathematicians...
194 KB (22,692 words) - 07:19, 2 June 2025
Fiber bundle Geodesic Levi-Civita connection Linear map Manifold Matrix Multivector Pseudotensor Spinor Vector Vector space Notable tensors Mathematicians...
28 KB (4,420 words) - 18:01, 26 May 2025
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...
25 KB (4,364 words) - 04:10, 17 May 2025
Fiber bundle Geodesic Levi-Civita connection Linear map Manifold Matrix Multivector Pseudotensor Spinor Vector Vector space Notable tensors Mathematicians...
187 KB (25,046 words) - 15:25, 3 June 2025
syndrome, a rare liver disorder Rotor (mathematics), an even-graded multivector used to produce rotations and some other affine transformations Curl...
2 KB (362 words) - 13:49, 5 December 2024
Fiber bundle Geodesic Levi-Civita connection Linear map Manifold Matrix Multivector Pseudotensor Spinor Vector Vector space Notable tensors Mathematicians...
67 KB (10,058 words) - 03:02, 23 March 2025
Fiber bundle Geodesic Levi-Civita connection Linear map Manifold Matrix Multivector Pseudotensor Spinor Vector Vector space Notable tensors Mathematicians...
37 KB (6,453 words) - 09:24, 15 May 2025
Jacobian determinant of a change-of-coordinate function. Grassmannian Multivector Exterior algebra Differential form Geometric algebra Clifford algebra...
7 KB (781 words) - 20:05, 25 March 2025
Fiber bundle Geodesic Levi-Civita connection Linear map Manifold Matrix Multivector Pseudotensor Spinor Vector Vector space Notable tensors Mathematicians...
46 KB (5,964 words) - 21:55, 19 May 2025
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...
8 KB (1,138 words) - 20:21, 19 January 2025
Fiber bundle Geodesic Levi-Civita connection Linear map Manifold Matrix Multivector Pseudotensor Spinor Vector Vector space Notable tensors Mathematicians...
11 KB (1,719 words) - 12:38, 26 May 2025
Fiber bundle Geodesic Levi-Civita connection Linear map Manifold Matrix Multivector Pseudotensor Spinor Vector Vector space Notable tensors Mathematicians...
112 KB (13,895 words) - 01:31, 4 June 2025
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...
75 KB (11,568 words) - 14:01, 8 May 2025
Fiber bundle Geodesic Levi-Civita connection Linear map Manifold Matrix Multivector Pseudotensor Spinor Vector Vector space Notable tensors Mathematicians...
31 KB (4,261 words) - 10:03, 13 April 2025
Fiber bundle Geodesic Levi-Civita connection Linear map Manifold Matrix Multivector Pseudotensor Spinor Vector Vector space Notable tensors Mathematicians...
43 KB (7,001 words) - 09:24, 10 March 2025