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product of tensors

См. также в других словарях:

  • Outer product — For outer product in geometric algebra, see exterior product. In linear algebra, the outer product typically refers to the tensor product of two vectors. The result of applying the outer product to a pair of vectors is a matrix. The name… …   Wikipedia

  • Tensor product — In mathematics, the tensor product, denoted by otimes, may be applied in different contexts to vectors, matrices, tensors, vector spaces, algebras, topological vector spaces, and modules. In each case the significance of the symbol is the same:… …   Wikipedia

  • Dot product — Scalar product redirects here. For the abstract scalar product, see Inner product space. For the operation on complex vector spaces, see Hermitian form. For the product of a vector and a scalar, see scalar multiplication. In mathematics, the dot… …   Wikipedia

  • Intermediate treatment of tensors — In mathematics and physics, a tensor is an idealized geometric or physical quantity whose numerical description, relative to a particular frame of reference, consists of a multiple indexed array of numbers. A vector, for example, is a tensor with …   Wikipedia

  • Classical treatment of tensors — A tensor is a generalization of the concepts of vectors and matrices. Tensors allow one to express physical laws in a form that applies to any coordinate system. For this reason, they are used extensively in continuum mechanics and the theory of… …   Wikipedia

  • Kulkarni–Nomizu product — In the mathematical field of differential geometry, the Kulkarni ndash;Nomizu product is defined for two (0,2) tensors and gives as a result a (0,4) tensor. If h and k are (0,2) tensors, then the product is defined via::hcirc k(X 1,X 2,X 3,X… …   Wikipedia

  • Cross product — This article is about the cross product of two vectors in three dimensional Euclidean space. For other uses, see Cross product (disambiguation). In mathematics, the cross product, vector product, or Gibbs vector product is a binary operation on… …   Wikipedia

  • Dyadic product — In mathematics, in particular multilinear algebra, the dyadic product of two vectors, and , each having the same dimension, is the tensor product of the vectors and results in a tensor of order two and rank one. It is also called outer product.… …   Wikipedia

  • Metric tensor — In the mathematical field of differential geometry, a metric tensor is a type of function defined on a manifold (such as a surface in space) which takes as input a pair of tangent vectors v and w and produces a real number (scalar) g(v,w) in a… …   Wikipedia

  • Symmetric algebra — In mathematics, the symmetric algebra S ( V ) (also denoted Sym ( V )) on a vector space V over a field K is the free commutative unital associative K algebra containing V .It corresponds to polynomials with indeterminates in V , without choosing …   Wikipedia

  • Tensor — For other uses, see Tensor (disambiguation). Note that in common usage, the term tensor is also used to refer to a tensor field. Stress, a second order tensor. The tensor s components, in a three dimensional Cartesian coordinate system, form the… …   Wikipedia

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