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searching for Exterior algebra 11 found (152 total)

Lagrange's identity (3,715 words) [view diff] no match in snippet view article find links to article

In algebra, Lagrange's identity, named after Joseph Louis Lagrange, is: ( ∑ k = 1 n a k 2 ) ( ∑ k = 1 n b k 2 ) − ( ∑ k = 1 n a k b k ) 2 = ∑ i = 1 n −

Fierz identity (797 words) [view diff] exact match in snippet view article find links to article

be obtained by expressing the Clifford algebra as a quotient of the exterior algebra[further explanation needed]. When working in 4 spacetime dimensions

E8 (mathematics) (6,105 words) [view diff] exact match in snippet view article

the exterior algebra over the 27 "covector" representation. The "vector" representation then lies, not in this nonnegative-graded exterior algebra, but

Supermanifold (2,112 words) [view diff] no match in snippet view article find links to article

^{\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

Noncommutative geometry (2,385 words) [view diff] exact match in snippet view article find links to article

It is constructed from a smooth vector bundle E over M, e.g. the exterior algebra bundle. The Hilbert space L2(M, E) of square integrable sections of

Super Minkowski space (2,131 words) [view diff] exact match in snippet view article find links to article

S{\displaystyle S} to be the representation constructed using the exterior algebra of some vector space, as described here. The complex dimension of S{\displaystyle

Projective geometry (5,092 words) [view diff] exact match in snippet view article find links to article

compilation of three notes by Cesare Burali-Forti on the application of exterior algebra to projective geometry C. Burali-Forti, "Introduction to Differential

Glossary of areas of mathematics (7,687 words) [view diff] exact match in snippet view article find links to article

investigate mathematical objects and identify properties and patterns. Exterior algebra Exterior calculus Extraordinary cohomology theory Extremal combinatorics

BRST quantization (8,856 words) [view diff] exact match in snippet view article find links to article

vector field. Longitudinal p {\displaystyle p} -forms are dual to the exterior algebra of p {\displaystyle p} -vectors. d {\displaystyle d} is essentially

Steenrod algebra (5,578 words) [view diff] exact match in snippet view article find links to article

{\displaystyle 2p^{k}-2} ( k ≥ 1 ) {\displaystyle (k\geq 1)} and the exterior algebra in generators τk of degree 2 p k − 1 {\displaystyle 2p^{k}-1} ( k ≥

Reed–Muller code (5,005 words) [view diff] exact match in snippet view article find links to article

wedge product (not to be confused with the wedge product defined in exterior algebra). Here, w = ( w 1 , w 2 , … , w N ) {\displaystyle w=(w_{1},w_{2},\ldots