View source for Contravariant vector

The name of an element of a vector space <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c025/c025980/c0259801.png" /> in the case when the dual (or conjugate) space (cf. [[Adjoint space|Adjoint space]]) <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c025/c025980/c0259802.png" /> is considered along with <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c025/c025980/c0259803.png" />. The elements of <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c025/c025980/c0259804.png" /> are then called covariant vectors (cf. [[Covariant vector|Covariant vector]]).



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