This is called a "covariant" transformation law, because the covector components transforms by the "same matrix" as the change of basis matrix. The components of a more general tensor transform by some combination of covariant and contravariant transformations, with one transformation law for each index. If the transformation matrix of an index is the inverse matrix of the basis transformation, then the index is called "contravariant" and is conventionally denoted with an upper index (superscript). If the transformation matrix of an index is the basis transformation itself, then the index is called "covariant" and is denoted with a lower index (subscript).