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A function is covariant when it commutes with the transformation, i.e.:
applying the transformation to the argument of the function has the same effect as applying the transformation to the output of the function.
See also: Function - Invariant
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Example
The orientation of the major axis of inertia of the surface is covariant under a rotation transformations, since rotating a 2D surface will affect the orientation of its major axis in exactly the same way.