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

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

between them. The n-dimensional generalization, the Grassmann number, was introduced by Hermann Grassmann in the late 19th century. In modern algebra, the...

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

are also "anticommuting" dimensions whose coordinates are labeled in Grassmann numbers rather than real numbers. The ordinary space dimensions correspond...

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

logical rigor in the foundations of mathematics. In the 1860s, Hermann Grassmann suggested a recursive definition for natural numbers, thus stating they...

Grassmann's laws describe empirical results about how the perception of mixtures of colored lights (i.e., lights that co-stimulate the same area on the...

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

Berezin, (also known as Grassmann integral, after Hermann Grassmann), is a way to define integration for functions of Grassmann variables (elements of...

usually called the Plücker relations, or Grassmann–Plücker relations, defining the intersection of a number of quadrics in P ( ⋀ k V ) {\displaystyle...

a bivector. Hestenes, David (1996). "Grassmann's Vision" (PDF). In Schubring, G. (ed.). Hermann Günther Graßmann (1809–1877). Springer. doi:10.1007/978-94-015-8753-2_20...

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

In graph theory, Grassmann graphs are a special class of simple graphs defined from systems of subspaces. The vertices of the Grassmann graph Jq(n, k) are...

1853, Grassmann published a theory of how colors mix; it and its three color laws are still taught, as Grassmann's law. As noted first by Grassmann... the...

Grassmann algebra and Hamilton's quaternion algebra. Adding the dual of the Grassmann exterior product (the "meet") allows the use of the Grassmann–Cayley...

term anti-commuting c-number is also used to refer to a type of anti-commuting numbers that are mathematically described by Grassmann numbers. The term is...

Operators. The symbol U+2229 ∩ INTERSECTION was first used by Hermann Grassmann in Die Ausdehnungslehre von 1844 as general operation symbol, not specialized...

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

{\displaystyle \alpha ,{\dot {\alpha }}=1,2} , where each component is a Grassmann number. In total this forms 4 spin coordinates. The notation for N = 1 {\displaystyle...

formalizing arithmetic was not well appreciated until the work of Hermann Grassmann, who showed in the 1860s that many facts in arithmetic could be derived...

pairings gives zero in this case (there are always an even number of them). This is the Grassmann analog of the higher Gaussian moments that completed the...

Graphical timeline of the universe Grashof condition Grashof number Grassmann integral Grassmann number Gravastar Gravimeter Gravimetry Graviphoton Graviscalar...

is the (real-number-valued) spacetime coordinate, and θ {\displaystyle \theta \,} and θ ¯ {\displaystyle {\bar {\theta }}} are Grassmann-valued spatial...

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

Minzer, Dor; Safra, Muli (2017). "On independent sets, 2-to-2 games, and Grassmann graphs". In Hatami, Hamed; McKenzie, Pierre; King, Valerie (eds.). Proceedings...

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

have properties similar to the homogeneous coordinates of points, called Grassmann coordinates. Points in a real projective space Pn are defined to be lines...

product come from Grassmann, while the words scalar, vector, scalar product, and vector product came from Hamilton. The disciples of Grassmann, in other ways...

British mathematician and philosopher. Building on the work of Hermann Grassmann, he introduced what is now termed geometric algebra, a special case of...