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Covariance and contravariance of vectors

In physics, especially in multilinear algebra and tensor analysis, covariance and contravariance describe how the quantitative description of certain geometric or physical entities changes with a change of basis. Briefly, a contravariant vector is a list of numbers that transforms oppositely to a change of basis, and a covariant vector is a list of…

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Definition

Coordinates

Covariant and contravariant components of a vector with a metric

Use in tensor analysis

Algebra and geometry

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Covariance and contravariance of vectors

Nodes81
Edges80
Triples0
Avg. degree1.98
Density0.024691
Components1

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vector displaystyle basis components mathbf contravariant covariant vectors end tensor change space begin cdot matrix coordinate dual transform product ij

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