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## Homework Statement

Assume that you want to the derivative of a vector

**V**with respect to a component Z

^{k}, the derivative is then ∂V

^{i}

**Z**/∂Z

_{i}^{k}=

**Z**

_{i}∂V

^{i}/∂Z

^{k}+V

^{i}∂

**Z**

_{i}/∂Z

^{k}=

**Z**

_{i}∂V

^{i}/∂Z

^{k}+V

^{i}Γ

^{m}

_{ik}

**Z**

_{m}Now why is it that I can change m to i and i to j in V

^{i}Γ

^{m}

_{ik}

**Z**

_{m}?