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A vector's components change scale inversely to changes in scale to the reference axes, and consequently a vector is called a contravariant tensor. A vector, which is an example of a contravariant tensor, has components that transform inversely to the transformation of the reference axes, (with example transformations including rotation and ...
In physics, a covariant transformation is a rule that specifies how certain entities, such as vectors or tensors, change under a change of basis. [1] The transformation that describes the new basis vectors as a linear combination of the old basis vectors is defined as a covariant transformation.
By the usual subtyping rule for function types, this means that the overriding method should return a more specific type (return type covariance) and accept a more general argument (parameter type contravariance). In UML notation, the possibilities are as follows (where Class B is the subclass that extends Class A which is the superclass):
Covariance and contravariance may refer to: Covariance and contravariance of vectors, in mathematics and theoretical physics; Covariance and contravariance of functors, in category theory; Covariance and contravariance (computer science), whether a type system preserves the ordering ≤ of types; An informal synonym for invariance (physics)
Instead covariance or contravariance refers to a given representation of the vector, depending on the basis being used. For example, one can write the same vector in either manner as, = =. I think this point (in addition to the variance topic as a whole) can be both subtle and confusing to people first learning these topics, and thus the ...
In general, the (transformational) nature of a Lorentz tensor [clarification needed] can be identified by its tensor order, which is the number of free indices it has.No indices implies it is a scalar, one implies that it is a vector, etc.
A vector-valued function, also referred to as a vector function, is a mathematical function of one or more variables whose range is a set of multidimensional vectors or infinite-dimensional vectors. The input of a vector-valued function could be a scalar or a vector (that is, the dimension of the domain could be 1 or greater than 1); the ...
A vector can be specified with covariant coordinates (lowered indices, written v k) or contravariant coordinates (raised indices, written v k). From the above vector sums, it can be seen that contravariant coordinates are associated with covariant basis vectors, and covariant coordinates are associated with contravariant basis vectors.