Summary
In differential geometry, components of a vector relative to a basis of the tangent bundle are covariant if they change with the same linear transformation as a change of basis
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, while they are contravariant if they change by the inverse transformation.
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A covariant tensor is a type of tensor with specific transformation properties that differ from those of a contravariant tensor.
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To turn a contravariant tensor into a covariant tensor, the metric tensor must be used.
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Summary
In differential geometry , the components of a vector relative to a basis of the tangent bundle are covariant if they change with the same linear transformation as a change of basis. They are contravariant if they change by the inverse transformation.
Covariance and contravariance of vectors - Wikipedia
wikipedia.org
Summary
A covariant tensor is a type of tensor with specific transformation properties that differ from those of a contravariant tensor. To turn a contravariant tensor into a covariant tensor, the metric tensor must be used. In Euclidean spaces, the metric tensor is constant, equal to Kronecker delta, and raising and lowering indices is trivial.
Covariant Tensor -- from Wolfram MathWorld
wolfram.com
Unable to generate a short snippet for this page, sorry about that.
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This tutorial explains Covariance and Contravariance in C#. Covariance and contravariance allow us to be flexible when dealing with class hierarchy.
Covariance and Contravariance in C#
tutorialsteacher.com
