Covariance
In probability theory and statistics, covariance is a measure of how much two random variables change together. If the greater values of one variable mainly correspond with the greater values of the other variable, and the same holds for the smaller values, i.e., the variables tend to show similar behavior, the covariance is positive. In the opposite case, when the greater values of one variable mainly correspond to the smaller values of the other, i.e., the variables tend to show opposite behavior, the covariance is negative. The sign of the covariance therefore shows the tendency in the linear relationship between the variables. The magnitude of the covariance is not easy to interpret. The normalized version of the covariance, the correlation coefficient, however, shows by its magnitude the strength of the linear relation.
A distinction must be made between (1) the covariance of two random variables, which is a population parameter that can be seen as a property of the joint probability distribution, and (2) the sample covariance, which serves as an estimated value of the parameter.
Covariance and contravariance (computer science)
The type system of many programming languages support subtyping. For instance, if Cat is subtype of Animal, then an expression of type Cat can be used whenever an expression of type Animal could. Variance refers to how subtyping between more complex types (list of Cats versus list of Animals, function returning Cat versus function returning Animal, ...) relates to subtyping between their components. Depending on the variance of the type constructor, the subtyping relation may be either preserved, reversed, or ignored. For example, in C#:
IEnumerable<Cat> is a subtype of IEnumerable<Animal>. The subtyping is preserved because IEnumerable<T> is covariant on T.Action<Animal> is a subtype of Action<Cat>. The subtyping is reversed because Action<T> is contravariant on T.IList<Cat> nor IList<Animal> is a subtype of the other, because IList<T> is invariant on T.The variance of a C# interface is determined by in/out annotations on its type parameters; the above interfaces are declared as IEnumerable<out T>, Action<in T>, and IList<T>. Types with more than one type parameter may specify different variances on each type parameter. For example, the delegate type Func<in T, out TResult> represents a function with a contravariant input parameter of type T and a covariant return value of type TResult.
Covariance (disambiguation)
In mathematics and physics, covariance is a measure of how much two variables change together, and may refer to:
Statistics
Algebra and geometry
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by Caverns
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Blackout
by: CavernsFreedom is earnt through sacrifice and bloodshed.
Perpetual motion, cycle after cycle, the wheel turns, as we recapitulate.
Disillusioned by a ticking clock, in truth we are the enemy.
Time will come to claim it’s prize, by leave with empty hands.
Regret built this prison, we must find the key,
or bend the bars to break free. Tired of safety, this security.
At the edge of the earth and we’ve found nothing,
years wasted chasing ghosts through city streets and broken homes,
has it led you to the path you have to walk,
our fee will burn blister and bleed before we make it home.
The smartest men of our generation will refuse to walk in their fathers footsteps.
Without direction, there is no progress.
Break the cycle, shatter the clocks, burn the calendars.