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trv
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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?
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?