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mathematics, the covariant derivative is a way of specifying a derivative along tangent vectors of a manifold. Alternatively, the covariant derivative is...

and a covariant vector is a list of numbers that transforms in the same way. Contravariant vectors are often just called vectors and covariant vectors...

is a subtype of "list of Animal" because the list type constructor is covariant. This means that the subtyping relation of the simple types is preserved...

Look up covariance or covariant in Wiktionary, the free dictionary. In mathematics and physics, covariance is a measure of how much two variables change...

In physics, a covariant transformation is a rule that specifies how certain entities, such as vectors or tensors, change under a change of basis. The...

In object-oriented programming, a covariant return type of a method is one that can be replaced by a "narrower" (derived) type when the method is overridden...

called covariant functors in order to distinguish them from contravariant ones. Note that one can also define a contravariant functor as a covariant functor...

In physics, the gauge covariant derivative is a means of expressing how fields vary from place to place, in a way that respects how the coordinate systems...

are used to label a variable object as covariant (lower index), contravariant (upper index), or mixed covariant and contravariant (having both upper and...

representation). An equation is said to be Lorentz covariant if it can be written in terms of Lorentz covariant quantities (confusingly, some use the term invariant...

In the mathematical field of differential geometry, the exterior covariant derivative is an extension of the notion of exterior derivative to the setting...

differential geometry and vector calculus, the second covariant derivative, or the second order covariant derivative, of a vector field is the derivative of...

The covariant formulation of classical electromagnetism refers to ways of writing the laws of classical electromagnetism (in particular, Maxwell's equations...

space that they do in flat space. A physical law expressed in a generally covariant fashion takes the same mathematical form in all coordinate systems, and...

i j . {\displaystyle {\hat {w}}_{i}=w_{j}R_{i}^{j}.} This is called a covariant transformation law, because the covector components transform by the same...

More generally a covariant is a polynomial in a0, ..., an, x, y that is invariant, so an invariant is a special case of a covariant where the variables...

matrix whose entries transform covariantly under changes to the coordinate system. Thus a metric tensor is a covariant symmetric tensor. From the coordinate-independent...

In general relativity, a manifestly covariant equation is one in which all expressions are tensors. The operations of addition, tensor multiplication...

no indices will be raised or lowered while retaining the base symbol, covariant indices are sometimes placed below contravariant indices for notational...

In Covariant Hamiltonian field theory, canonical momenta pμi corresponds to derivatives of fields with respect to all world coordinates xμ. Covariant Hamilton...