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## Main Question or Discussion Point

**Note: The derivatives are partial.**

I've seen the coordinate transformation equation for contravariant vectors given as follows,

V'

^{a}=(dX'

^{a}/dX

^{b})V

^{b}

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}/dX

^{a})V

^{a}

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?