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 [ˈhɛʁman ˈɡʏntɐ ˈɡʁasman]; 15 April 1809 – 26 September 1877) was a German polymath known in his...

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

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

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

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

terms, because the square of a Grassmann number is zero, and there are exactly n {\displaystyle n} distinct Grassmann variables. Meanwhile, the integral...

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...

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

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

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...

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

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...

a bivector. Hestenes, David (1996). "Grassmann's Vision" (PDF). In Schubring, G. (ed.). Hermann Günther Graßmann (1809–1877). Boston Studies in the Philosophy...

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...

{\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...

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

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

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

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

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...

Billboard Hot 100 top five singles, including two number-ones. Iglesias holds the record for the most number-one songs on the Billboard Hot Latin Songs chart...

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...

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

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

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

of p-vectors and multivectors with Grassmann algebra. Multiplicative number theory a subfield of analytic number theory that deals with prime numbers...

(red) light (accounting for luminosity). In 1853, Hermann Grassmann developed Grassmann's laws, which aimed to describe color mixing algebraically. These...

and Schläfli's discovery of the 4-polytopes, Möbius (with Cayley and Grassmann) was one of only three other people who had also conceived of the possibility...