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^{μ}= ∂x

^{μ}/∂x

^{ν}V

^{ν}. However, dual vectors are members of vector spaces (cotangent space) but obey ω

_{μ}= ∂x

^{v}/∂x

^{μ}ω

_{v}. Is this abuse of terminology? If so, what is a more exact way of describing objects in vector spaces obeying the vector transformation law?