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searching for tensor algebra 22 found (182 total)

Algebra bundle (194 words) [view diff] no match in snippet view article find links to article

spaces, every algebra bundle is a vector bundle. Examples include the tensor-algebra bundle, exterior bundle, and symmetric bundle associated to a given

Tensor software (2,065 words) [view diff] exact match in snippet view article find links to article

purpose computer algebra system which includes several packages for tensor algebra calculations in its core distribution. It is particularly useful for

The Classical Groups (495 words) [view diff] exact match in snippet view article find links to article

classical group action; second, the isotypic decomposition of the full tensor algebra for such an action. 1Most people who know the book feel the material

Leibniz algebra (695 words) [view diff] exact match in snippet view article find links to article

over an associative R-algebra A then the Leibniz homology of L is the tensor algebra over the Hochschild homology of A. A Zinbiel algebra is the Koszul dual

Curvilinear coordinates (8,311 words) [view diff] exact match in snippet view article find links to article

determine the position of this point in a unique way. Elementary vector and tensor algebra in curvilinear coordinates is used in some of the older scientific literature

Kaluza–Klein theory (7,301 words) [view diff] no match in snippet view article find links to article

curvature tensors for the complete Kaluza equations were evaluated using tensor-algebra software in 2015, verifying results of J. A. Ferrari and R. Coquereaux

Kontsevich invariant (938 words) [view diff] exact match in snippet view article find links to article

Jacobi diagram can be viewed as abstraction of representations of the tensor algebra generated by Lie algebras, which allows us to define some operations

Dimension (vector space) (1,485 words) [view diff] case mismatch in snippet view article

choice see dimension theorem for vector spaces Itzkov, Mikhail (2009). Tensor Algebra and Tensor Analysis for Engineers: With Applications to Continuum Mechanics

Coproduct (2,130 words) [view diff] exact match in snippet view article find links to article

of (noncommutative) R-algebras, the coproduct is a quotient of the tensor algebra (see Free product of associative algebras). In the case of topological

Lie coalgebra (1,115 words) [view diff] exact match in snippet view article find links to article

^{3}E\xrightarrow {d} \ \cdots } Just as the exterior algebra (and tensor algebra) of vector fields on a manifold form a Lie algebra (over the base field

Robert Hermann (mathematician) (945 words) [view diff] exact match in snippet view article

in General Relativity 1973: Energy-Momentum Tensors 1973: Linear and tensor algebra 1974: Spinors, Clifford and Cayley Algebras 1974: Linear systems and

Curvature of Riemannian manifolds (2,115 words) [view diff] exact match in snippet view article find links to article

They give rise to a tensor only by identifications with objects of the tensor algebra – but likewise there are identifications with concepts in the Clifford-algebra

Zener ratio (1,102 words) [view diff] exact match in snippet view article find links to article

(AU)' was formulated from variational principles of elasticity and tensor algebra. The AU is now used to quantify the anisotropy of elastic crystals of

Monoidal category (2,436 words) [view diff] exact match in snippet view article find links to article

1993.1055. Joyal, André; Street, Ross (1988). "Planar diagrams and tensor algebra" (PDF). Kelly, G. Max (1964). "On MacLane's Conditions for Coherence

Wightman axioms (2,719 words) [view diff] exact match in snippet view article find links to article

state called a Wightman functional on a Borchers algebra equal to the tensor algebra of a space of test functions. One can generalize the Wightman axioms

Mode-k flattening (491 words) [view diff] exact match in snippet view article find links to article

inefficient way to matrixize.[citation needed] This operation is used in tensor algebra and its methods, such as Parafac and HOSVD.[citation needed] Vasilescu

String diagram (3,699 words) [view diff] exact match in snippet view article find links to article

07055 [cs.LO]. Joyal, André; Street, Ross (1988). "Planar diagrams and tensor algebra". Unpublished Manuscript, Available from Ross Street's Website. Vicary

Optical computing (3,440 words) [view diff] case mismatch in snippet view article find links to article

PC Gamer. Retrieved 2023-07-02. Redrouthu, Sathvik (2022-08-13). "Tensor Algebra on an Optoelectronic Microchip". arXiv:2208.06749 [cs.PL]. de Wolff

Serre's theorem on a semisimple Lie algebra (1,346 words) [view diff] exact match in snippet view article find links to article

∞ V ⊗ l {\textstyle T=\bigoplus _{l=0}^{\infty }V^{\otimes l}} the tensor algebra over it. Consider the following representation of a Lie algebra: π :

Dirac algebra (2,342 words) [view diff] exact match in snippet view article find links to article

generalization of the exterior algebra: both arise as quotients of the tensor algebra, but the exterior algebra gives a more restrictive quotient, where the

Pure spinor (2,923 words) [view diff] exact match in snippet view article find links to article

algebra C l ( V , Q ) {\displaystyle Cl(V,Q)} is the quotient of the full tensor algebra on V {\displaystyle V} by the ideal generated by the relations u ⊗ v

Lorentz transformation (14,794 words) [view diff] exact match in snippet view article find links to article

way which also illustrates the unit of the electromagnetic field uses tensor algebra, given below. Throughout, italic non-bold capital letters are 4 × 4