In
mathematics
Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many ar ...
and
physics
Physics is the scientific study of matter, its Elementary particle, fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge whi ...
,
covariance is a measure of how much two
variables change together, and may refer to:
Statistics
*
Covariance matrix, a matrix of covariances between a number of variables
*
Covariance or
cross-covariance between two random variables or data sets
*
Autocovariance, the covariance of a signal with a time-shifted version of itself
*
Covariance function
In probability theory and statistics, the covariance function describes how much two random variables change together (their ''covariance'') with varying spatial or temporal separation. For a random field or stochastic process ''Z''(''x'') on a dom ...
, a function giving the covariance of a random field with itself at two locations
Algebra and geometry
* A
covariant (invariant theory) is a bihomogeneous polynomial in and the coefficients of some homogeneous form in that is invariant under some group of linear transformations.
*
Covariance and contravariance of vectors, properties of how vector coordinates change under a change of basis
**
Covariant transformation, a rule that describes how certain physical entities change under a change of coordinate system
*
Covariance and contravariance of functors, properties of functors
*
General covariance
In theoretical physics, general covariance, also known as diffeomorphism covariance or general invariance, consists of the Invariant (physics), invariance of the ''form'' of physical laws under arbitrary Derivative, differentiable coordinate transf ...
or simply covariance (inaccurate but common usage in quantum mechanics), the invariance of the mathematical form of physical laws under arbitrary differential coordinate transformations (including Lorentz transformations), strictly meaning ''invariance''
*
Lorentz covariance, a property of space-time that follows from the special theory of relativity
**
Poincaré covariance, a related property
*
Eddy covariance, an atmospheric flux measurement technique
* in category theory,
covariant functor, the same as a functor (the term is used to be in contrast to the term
contravariant functor).
Computer science
*
Covariance and contravariance (computer science), a system of class relations in computer science
See also
*
Covariance and correlation
*
Covariance and contravariance (disambiguation)
{{Mathematical disambiguation