In mathematics, the exterior algebra or Grassmann algebra of a vector space V {\displaystyle V} is an associative algebra that contains V , {\displaystyle...

Hermann Günther Grassmann (German: Graßmann, pronounced [ˈhɛɐman ˈɡʏntʰɐ ˈɡʁasman]; 15 April 1809 – 26 September 1877) was a German polymath known in...

physics, a Grassmann number, named after Hermann Grassmann (also called an anticommuting number or supernumber), is an element of the exterior algebra of a...

Clifford algebra and its product as a unification of the Grassmann algebra and Hamilton's quaternion algebra. Adding the dual of the Grassmann exterior...

In mathematics, a Grassmann–Cayley algebra is the exterior algebra with an additional product, which may be called the shuffle product or the regressive...

Any commutative algebra is a supercommutative algebra if given the trivial gradation (i.e. all elements are even). Grassmann algebras (also known as exterior...

manipulation is carried out using exterior algebra. Following Grassmann, developments in multilinear algebra were made by Victor Schlegel in 1872 with...

subtle structure than the Grassmann numbers. So, the Grassmann numbers are elements of the exterior algebra, and the Clifford algebra has an isomorphism to...

Hermann Grassmann: Grassmann's laws Grassmann algebra Grassmann bundle Grassmann dimensions Grassmann graph Grassmann integral Grassmann number Grassmann variables...

spatial Fourier transform of the Dirac field as a new basis for the Grassmann algebra, the quadratic part of the Dirac action becomes simple to invert:...

1844 Hermann Grassmann published his "Theory of Extension" which included foundational new topics of what is today called linear algebra. In 1848, James...

V ) {\displaystyle \mathbf {Gr} _{k}(V)} (named in honour of Hermann Grassmann) is a differentiable manifold that parameterizes the set of all k {\displaystyle...

supercommutative algebra (or ring). A common construction when working with super vector spaces is to enlarge the field of scalars to a supercommutative Grassmann algebra...

Gerstenhaber algebra Anyonic Lie algebra Grassmann algebra Representation of a Lie superalgebra Superspace Supergroup Universal enveloping algebra See Deligne's...

père et fils Grassmann, Hermann (1844), Die Lineale Ausdehnungslehre - Ein neuer Zweig der Mathematik (in German), reprint: Hermann Grassmann. Translated...

Grassmann integral, after Hermann Grassmann), is a way to define integration for functions of Grassmann variables (elements of the exterior algebra)...

In mathematics, the tensor algebra of a vector space V, denoted T(V) or T•(V), is the algebra of tensors on V (of any rank) with multiplication being the...

cohomology Multilinear algebra an extension of linear algebra building upon concepts of p-vectors and multivectors with Grassmann algebra. Multiplicative number...

Schönberg's papers of 1956 and 1957 as described in section "The Grassmann–Schönberg algebra Gn" of Bolivar 2001 See for ex. Oziewicz & Sitarczyk 1992 Clifford...

space). The image of that embedding is the Klein quadric in RP5. Hermann Grassmann generalized Plücker's embedding to arbitrary k and n. The homogeneous...

power distributions can be algebraically related to one another in a color matching context. Discovered by Hermann Grassmann these "laws" are actually...

was published in 2016 and is now known for its unique treatment of Grassmann algebra. The second volume, covering a wide range of rendering topics, was...

be called Grassmann variables or Grassmann directions; they are generators of the exterior algebra of anti-commuting numbers, the Grassmann numbers. All...

examples are those with entries in a commutative superalgebra (such as a Grassmann algebra) or an ordinary field (thought of as a purely even commutative superalgebra)...

for manipulations of tensors arise as an extension of linear algebra to multilinear algebra. In differential geometry, an intrinsic[definition needed] geometric...

^{\bullet }(\xi _{1},\dots \xi _{q})} , where the latter is a Grassmann (Exterior) algebra on q generators. A supermanifold M of dimension (1,1) is sometimes...

space Lagrangian Grassmannian Grassmann algebra, or exterior algebra, a setting where the exterior product is defined. Grassmann number, a construction for...

quaternions (due to Hamilton), Grassmann's Ausdehnungslehre, and Boole's algebra of logic. Whitehead wrote in his book: "Such algebras have an intrinsic value...

root for every nonconstant polynomial exists (see Algebraic closure and Fundamental theorem of algebra). Here, the term "imaginary" is used because there...

on the work of Hermann Grassmann, he introduced what is now termed geometric algebra, a special case of the Clifford algebra named in his honour. The...