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- However, Sather supported both covariance and contravariance.
- The mathematically precise way this happens is detailed at covariance and contravariance of vectors.
- See also Covariance and contravariance of vectors.
- Contravariance captures the physical intuition behind the idea that a vector has " magnitude and direction ".
- :The connoisseurs will undoubtedly point out that I have played a bit loose with the covariance and contravariance.
- :Covariance and contravariance ( computer science ) is the Wikipedia article about this, though it could stand improvement.
- In some advanced contexts, a row and a column vector have different meaning; see covariance and contravariance of vectors.
- The distinction between covariance and contravariance is particularly important for computations with tensors, which often have "'mixed variance " '.
- On the other hand, programmers often find contravariance unintuitive, and accurately tracking variance to avoid runtime type errors can lead to complex typing rules.
- In tensor analysis, superscripts are used instead of subscripts to distinguish covariant from contravariant entities, see covariance and contravariance of vectors and raising and lowering indices.