contravariant index

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• Index notation — is used in mathematics to refer to the elements of matrices or the components of a vector. The formalism of how indices are used varies according to the discipline. In particular, there are different methods for referring to the elements of a… …   Wikipedia

• Abstract index notation — is a mathematical notation for tensors and spinors that uses indices to indicate their types, rather than their components in a particular basis. The indices are mere placeholders, not related to any fixed basis, and in particular are non… …   Wikipedia

• Tetrad (index notation) — In Riemannian geometry, we can introduce a coordinate system over the Riemannian manifold (at least, over a chart), giving n coordinates :xi, i=1,...,n for an n dimensional manifold. Locally, at least, this gives a basis for the 1 forms, dxi… …   Wikipedia

• Tensor contraction — In multilinear algebra, a tensor contraction is an operation on one or more tensors that arises from the natural pairing of a finite dimensional vector space and its dual. In components, it is expressed as a sum of products of scalar components… …   Wikipedia

• Mixed tensor — In tensor analysis, a mixed tensor is a tensor which is neither strictly covariant nor strictly contravariant; at least one of the indices of a mixed tensor will be a subscript (covariant) and at least one of the indices will be a superscript… …   Wikipedia

• Kronecker delta — In mathematics, the Kronecker delta or Kronecker s delta, named after Leopold Kronecker (1823 1891), is a function of two variables, usually integers, which is 1 if they are equal, and 0 otherwise. So, for example, delta {12} = 0, but delta {33} …   Wikipedia

• Covariance and contravariance of vectors — For other uses of covariant or contravariant , see covariance and contravariance. In multilinear algebra and tensor analysis, covariance and contravariance describe how the quantitative description of certain geometric or physical entities… …   Wikipedia

• Covariant transformation — See also Covariance and contravariance of vectors In physics, a covariant transformation is a rule (specified below), that describes how certain physical entities change under a change of coordinate system. In particular the term is used for… …   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

• Euclidean vector — This article is about the vectors mainly used in physics and engineering to represent directed quantities. For mathematical vectors in general, see Vector (mathematics and physics). For other uses, see vector. Illustration of a vector …   Wikipedia

• Change of basis — In linear algebra, change of basis refers to the conversion of vectors and linear transformations between matrix representations which have different bases. Contents 1 Expression of a basis 2 Change of basis for vectors 2.1 Tensor proof …   Wikipedia