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covariant 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

  • Covariant derivative — In mathematics, the covariant derivative is a way of specifying a derivative along tangent vectors of a manifold. Alternatively, the covariant derivative is a way of introducing and working with a connection on a manifold by means of a… …   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

  • 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

  • Mathematics of general relativity — For a generally accessible and less technical introduction to the topic, see Introduction to mathematics of general relativity. General relativity Introduction Mathematical formulation Resources …   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

  • 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

  • Connection (vector bundle) — This article is about connections on vector bundles. See connection (mathematics) for other types of connections in mathematics. In mathematics, a connection on a fiber bundle is a device that defines a notion of parallel transport on the bundle; …   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

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