e/Covariance and contravariance of vectors

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has glosseng: * For a vector (such as a direction vector or velocity vector) to be coordinate system invariant, the components of the vector must contra-vary with a change of basis to compensate. That is, the components must vary in the opposite "direction" (the inverse transformation) as the change of basis. Vectors (as opposed to dual vectors) are said to be contravariant. Examples of contravariant vectors include the position of an object relative to an observer, or any derivative of position with respect to time, including velocity, acceleration, and jerk. In Einstein notation, contravariant components have upper indices as in :\mathbfv} = \mathbfe}_i v^i.
lexicalizationeng: Covariance and contravariance of vectors
instance ofe/Tensor
Meaning
French
has glossfra: Les coordonnées x_j et x_i dun vecteur ou dun tenseur dans ces bases, sont dites covariantes lorsquelles « varient comme » les vecteurs de base, cest à dire lorsque lon a :
lexicalizationfra: Covariance et contravariance
Italian
has glossita: Nell'algebra multilineare e nel calcolo tensoriale, le componenti covarianti e controvarianti dei vettori descrivono i cambiamenti di certe entità geometriche o fisiche quando si passa da un sistema di coordinate ad un altro.
lexicalizationita: componenti covarianti e controvarianti
Castilian
has glossspa: Covariancia y contravariancia son conceptos empleados frecuentemente en áreas de la matemática y la física teórica. Por regla general se refieren a que ciertos objetos matemáticos, que pueden representar alguna magnitud física, tienen alguna forma de invariancia de forma, es decir, la propiedad de permanecer sin cambio bajo un conjunto dado de transformaciones.
lexicalizationspa: Covariancia y contravariancia
Swedish
has glossswe: Kontravariant vektor kallas inom allmän relativitetsteori en vektor med index uppe, \; x^a. Att en vektor har index uppe eller nere har enbart matematisk betydelse.
lexicalizationswe: kontravariant vektor
Chinese
has glosszho: 在理論物理,反變(contravariant)和共變(covariant)指描述了一個向量或(更廣義來說,張量)的座標,在向量空間的基/座標系轉換之下,會如何改變。
lexicalizationzho: 共變和反變
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media:imgBasis.gif

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