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Tensor calculus (tensor analysis) is a systematic extension of vector calculus to multivector and tensor fields in a form that is independent of the choice of coordinates on the relevant manifold, but which accounts for respective sub-spaces, their symmetries, and their connections.

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Levi Civita identity

I've been trying to use the following identity (provided by wikipedia) $$\epsilon^{i_1...i_n}\epsilon_{j_1...j_n} = \delta_{j_1...j_n}^{i_1...i_n} \equiv n!\delta_{[j_1}^{i_1}...\delta_{j_n]}^{i_n}$$ …
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