# covariant and contravariant

## 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 1 , while they are contravariant if they change by the inverse transformation. 1 A covariant tensor is a type of tensor with specific transformation properties that differ from those of a contravariant tensor. 2 To turn a contravariant tensor into a covariant tensor, the metric tensor must be used. 2

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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

Learn about covariance, which allows you to use a more derived type, and contravariance, ... In general, a covariant type parameter can be used as the return ...
Covariance and Contravariance in Generics | Microsoft Docs
microsoft.com

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

Learn about covariance and contravariance and how they affect assignment compatibility. ... is called variant if its generic parameters are declared covariant ...
Covariance and Contravariance (C#) | Microsoft Docs
microsoft.com

mathpages.com

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

A contravariant tensor is a tensor having specific transformation properties (cf., a covariant tensor). To examine the transformation properties of a ...
Contravariant Tensor -- from Wolfram MathWorld
wolfram.com

Covariance and Contravariance in C# sounds like advanced concepts. However you use them ... generic interface or generic delegate type can have both covariant ...
Covariance and Contravariance in C# Explained - NDepend
ndepend.com

Subtyping is a tricky topic in programming language theory. The trickiness comes from a pair of frequently misunderstood phenomena called *covariance*...
What are covariance and contravariance? | Stephan Boyer
stephanboyer.com

Learn about covariance, which allows you to use a more derived type, and contravariance, ... In general, a covariant type parameter can be used as the return ...
Covariance and Contravariance in Generics | Microsoft Learn
microsoft.com

No, because user expects to be able to pass any kind of Mammal into f , not just Cat s. So function parameters are not covariant. On the other hand, it should ...
Covariance and contravariance in subtyping - Eli Bendersky's website
thegreenplace.net