Note: The derivatives are partial. I've seen the coordinate transformation equation for contravariant vectors given as follows, V'a=(dX'a/dXb)Vb What I don't get is the need for two indices a and b. Wouldn't it be adequate to just write the equation as follows? V'a=(dX'a/dXa)Va The prime being adequate to indicate the new and the unprimed the old, coordinates and contravariant vector. Or does the second index provide some more information which I am unaware of?