Contravariant vector

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The name of an element of a vector space $E$ in the case when the dual (or conjugate) space (cf. Adjoint space) $E^*$ is considered along with $E$. The elements of $E^*$ are then called covariant vectors (cf. Covariant vector).


The word "vector" or the phrase "contravariant vector" is also used to denote a vector field. Cf. also Tensor on a vector space; Contravariant tensor; Tensor bundle.

How to Cite This Entry:
Contravariant vector. Encyclopedia of Mathematics. URL:
This article was adapted from an original article by M.I. Voitsekhovskii (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article