Examples of 'contravariant' in a sentence
Meaning of "contravariant"
In mathematics, contravariant refers to the way objects or structures change with respect to a change in direction or orientation
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- which reverses composition
- Using or relating to contravariance.
- A bihomogeneous polynomial in dual variables of x, y, ... and the coefficients of some homogeneous form in x, y, ... that is invariant under some group of linear transformations.
How to use "contravariant" in a sentence
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contravariant
Contravariant functors are also occasionally called cofunctors.
Representation of covariant and contravariant components of a vector.
They are contravariant if they change by the inverse transformation.
The upper indices indicate contravariant components.
So the contravariant rule is not safe.
Notice that both indices of the components are contravariant.
The respective contravariant components with the conditions eq.
The needed transformation of v is called the contravariant transformation rule.
Contravariant and two covariant indices.
Vector fields are contravariant rank one tensor fields.
Contravariant argument type.
Vectors are therefore contravariant.
The proof in the contravariant case is completely analogous.
The assignment of the dual space to a vector space is a standard example of a contravariant functor.
Note that contravariant functors reverse the direction of composition.
See also
Similar statements apply when the two indices are contravariant or are mixed covariant and contravariant.
Contravariant indices can be turned into covariant indices by contracting with the metric tensor.
Are named contravariant.
Ordinary functors are also called covariant functors in order to distinguish them from contravariant ones.
This means that the contravariant elements are the directly inverse of the covariant components.
These terms come from the notion of covariant and contravariant functors in category theory.
Superscripts are contravariant indices in this section rather than exponents except when they indicate a square.
Composing this with the forgetful functor we have a contravariant functor from C to Set.
If F and G are contravariant functors one speaks of a duality of categories instead.
Covariant and Contravariant.
Contravariant components of the stress-energy tensor.
A presheaf on a topological space X is a contravariant functor from the category of open subsets to sets.
In category theory, there are covariant functors and contravariant functors.
Divide is the Contravariant analogue of Apply.
The components of vectors ( as opposed to those of covectors ) are said to be contravariant.
Examples of contravariant vectors include displacement, velocity and acceleration.
For this reason, it is said that ordinary vectors are contravariant objects.
The electric current is a contravariant vector density, and as such it transforms as follows:.
This shows that the interface is not allowed to be marked either co - or contravariant.
Analogous formulas also hold for contravariant tensors, as well as tensors of mixed variance.
In this context, for instance, a system of simultaneous equations is contravariant in the variables.
In other words, there is a contravariant functor that gives an equivalence between the categories.
For example, vectors change with its inverse and they are therefore called contravariant objects.
For instance, simplicial sets are contravariant with the codomain category being the category of sets.
Contravariant objects such as differential forms restrict to submanifolds, giving a mapping in the other direction.
In Dirac representation, the four contravariant gamma matrices are.
Of a K-fold contravariant Riemannian tensor field. This is the locally euclidean metrization.
Kronecker delta Levi-Civita symbol Covariant tensor Contravariant tensor The classical interpretation is by components.
Contravariant (source) positions cause problems.
A presheaf on a category is a contravariant functor from " C " to the category of all sets.
If λu > 1, the program continues to the calculation step 54 for determination of the contravariant eigenvectors.
Both covariant and contravariant four-vectors can be Lorentz covariant quantities.
It 's the Euclidean metrisation of a K-fold contravariant tensor field.
Note that Hk is a contravariant functor while Hn - k is covariant.
Thus we see that the functor Hom ( -, H ) is a contravariant functor.
