What are covariant and contravariant tensors?
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.
What are contravariant tensors?
A contravariant tensor is a tensor having specific transformation properties (cf., a covariant tensor). To examine the transformation properties of a contravariant tensor, first consider a tensor of rank 1 (a vector)
Can we add covariant and contravariant tensor?
Covariant and contravariant indices can be used simultaneously in a mixed tensor. Therefore, raising and lowering indices is trivial, hence covariant and contravariant tensors have the same coordinates, and can be identified.
What is the difference between covariance and contravariance?
Covariance permits a method to have a return type that is a subtype of the one defined in the delegate. Contravariance permits a method to have a parameter type that is a base type of the one defined in the delegate type.
What is the meaning of contravariant?
Adjective. contravariant (not comparable) (category theory, of a functor) which reverses composition.
What is meant by covariance and Contravariance?
Covariance and contravariance are terms that refer to the ability to use a more derived type (more specific) or a less derived type (less specific) than originally specified. Generic type parameters support covariance and contravariance to provide greater flexibility in assigning and using generic types.
What is the difference between covariance and Contravariance?
Is metric tensor A covariant contravariant?
Also, the contravariant (covariant) forms of the metric tensor are expressed as the dot product of a pair of contravariant (covariant) basis vectors. Two vectors may be multiplied in the manner of a dot product, which produces a scalar, or in the manner of a cross product that produces another vector.
What does contravariance mean?
contravariance (countable and uncountable, plural contravariances) (object-oriented programming) The reversal of the order of data types acted upon by an operator. quotations ▼coordinate term ▼ (category theory) A functor which reverses composition.
What is covariance in OOP?
Covariance means that a method can return a type that is derived from the delegate’s return type. Contra-variance means that a method can take a parameter that is a base of the delegate’s parameter type.
What is meant by covariance and contravariance?