 The transformation properties of vectors distinguish a vector as a geometrically distinct entity from a simple list of scalars, or from a covector.Thus, suppose that ("x"1...,"x""n") is a choice of Cartesian coordinates, in terms of which the components of the vector "V" are

and suppose that ("y"1...,"y""n") are "n" functions of the "x""i" defining a different coordinate system.Then the components of the vector "V" in the new coordinates are required to satisfy the transformation law
Such a transformation law is called contravariant.