exterior algebra in a sentence
1) It is a grade 1 derivation on the exterior algebra .
algebra collocations
2) This means that the exterior algebra is a graded algebra.
3) Clifford algebras are closely related to exterior algebras .
exterior algebra example sentences
4) More general exterior algebras can be defined for sheaves of modules.5) The exterior algebra provides an algebraic setting in which to answer geometric questions.
6) This book contains applications of exterior algebras to problems in partial differential equations.
7) With the rise of differential geometry the exterior algebra was applied to differential forms.
8) This extends by linearity to an operation defined on the whole exterior algebra .
9) Let denote the exterior algebra of "W" considered as vector space only.
10) It is defined on the exterior algebra of a finite-dimensional oriented inner product space.
11) The exterior algebra of the dual vector space Λ("V"*).
12) If "V" is finite-dimensional, then these two exterior algebras are naturally isomorphic.
13) An introduction to the exterior algebra , and geometric algebra, with a focus on applications.
14) The exterior algebra also has many algebraic properties that make it a convenient tool in algebra itself.
15) The exterior algebra has notable applications in differential geometry, where it is used to define differential forms.
example sentences with exterior algebra
16) In exterior algebra the exterior product (or wedge product) of two vectors is a bivector.17) Contains a classical treatment of the exterior algebra as alternating tensors, and applications to differential geometry.
18) With an antipode defined on homogeneous elements by , the exterior algebra is furthermore a Hopf algebra.
19) The codifferential is not an antiderivation on the exterior algebra , in contrast to the exterior derivative.
20) Includes applications of the exterior algebra to differential forms, specifically focused on integration and Stokes's theorem.
21) For vectors in R3, the exterior algebra is closely related to the cross product and triple product.
22) Then "A" (as an algebra) is a free exterior algebra with generators of odd degree.
23) This textbook in multivariate calculus introduces the exterior algebra of differential forms adroitly into the calculus sequence for colleges.
24) Forcing two such elements to be equal leads to the symmetric algebra, whereas forcing __FORMULA__ yields the exterior algebra .
25) The exterior algebra is the main ingredient in the construction of the Koszul complex, a fundamental object in homological algebra.
26) The exterior algebra , or Grassmann algebra after Hermann Grassmann, is the algebraic system whose product is the exterior product.
27) The wedge products of elements of an orthonormal basis in __FORMULA__ form an orthonormal basis of the exterior algebra of __FORMULA__.
28) The coproduct and counit, along with the exterior product, define the structure of a bialgebra on the exterior algebra .
How to use exterior algebra in a sentence
29) In particular, the exterior derivative gives the exterior algebra of differential forms on a manifold the structure of a differential algebra.30) Bivectors are quantities from geometric algebra, clifford algebra and the exterior algebra , which generalise the idea of vectors into two dimensions.
31) The bivector was first defined in 1844 by German mathematician Hermann Grassmann in exterior algebra as the result of the exterior product of two vectors.
32) In mathematics, a bivector or 2-vector is a quantity in exterior algebra or geometric algebra that extends the idea of scalars and vectors.
33) The Hodge dual extends this duality within an inner product space by providing a canonical correspondence between the elements of the exterior algebra .
34) The Hodge star defines a dual in that when it is applied twice, the result is an identity on the exterior algebra , up to sign.
35) The Hodge dual induces an inner product on the space of __FORMULA__-vectors, that is, on the exterior algebra of __FORMULA__.
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