• 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
  • 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
  • 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
  • Thumbnail for Exterior algebra
    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
  • Thumbnail for Transpose
    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
  • Thumbnail for Pseudovector
    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
  • Thumbnail for Tensor
    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
  • Thumbnail for Vector projection
    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
  • Thumbnail for Cauchy's integral formula
    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
  • Thumbnail for Special relativity
    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
  • Thumbnail for Differential geometry
    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
  • Thumbnail for Matrix (mathematics)
    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
  • Thumbnail for Cross product
    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
  • Thumbnail for Geodesic
    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