# Coordinate transformation of contravariant vectors.

 P: 898 The first equation has on the LHS a single component of V' while the RHS is a sum by summation convention over all the unprimed components. $$V'^1 = \frac{\partial X'^1}{\partial X^1}V^1 + \cdots + \frac{\partial X'^1}{\partial X^n}V^n\\ \vdots V'^m = \frac{\partial X'^m}{\partial X^1}V^1 + \cdots + \frac{\partial X'^m}{\partial X^n}V^n$$ Your equation is a single component and represents no sum, so it is not equivalent. $$V'^1 = \frac{\partial X'^1}{\partial X^1}V^1 \vdots V'^m = \frac{\partial X'^m}{\partial X^m}V^m$$ It seems to state that the ath component of V' depends only on the ath component of V, which is usually not the case.