covariant
Speech parts
1. covariant - Noun
2. covariant - Adjective
3. covariant - Adjective Satellite
Meaning
A function involving the coefficients and the variables of a quantic, and such that when the quantic is lineally transformed the same function of the new variables and coefficients shall be equal to the old function multiplied by a factor. An invariant is a like function involving only the coefficients of the quantic.
Source: Webster's dictionarySynonyms
Antonyms
Examples
A notable exception to modern algebraic geometry texts following the conventions of this article is Commutative algebra with a view toward algebraic geometry / David Eisenbud (1995), which uses "h A " to mean the covariant hom-functor.
Chapter six gives a "from scratch" introduction to covariant tensors.
For the individual matrix entries, this transformation law has the form so the tensor corresponding to the matrix of a linear operator has one covariant and one contravariant index: it is of type (1,1).
Given an arbitrary contravariant functor G from C to Set, Yoneda's lemma asserts that : Naming conventions The use of "h A " for the covariant hom-functor and "h A " for the contravariant hom-functor is not completely standard.
Covariant vectors There are also vector quantities with covariant indices.
He gave up looking for fully generally covariant tensor equations, and searched for equations that would be invariant under general linear transformations only.