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1. ### A Exploring Wedge Product of 0-Form and l-Form

Well I weren't sure how to cope with the $$\sigma.$$ My idea was to say that we find for every permutation a counter part, that deviates only by one transposition from our permutation, so to say its form might be $$\sigma \circ \tau,$$ wehere tau is a transposition. By the alternation of the...

8. ### I Explanation of the Alternator

Hello, let us define the Alternator $$Alt(T)$$ where T is a multilinear function $$Alt(T):= \frac{1}{k!} \sum_{\sigma \in S_n} sgn(\sigma) T (v_{\sigma(1)},...,v_{\sigma(k)}))$$. Further recognize that $$S_n$$ is the group of permutations and sgn the signum of the permutation. May...
9. ### A Coefficients in the linear combination of a k-form

Hello, I have another question in this context. Let us say we want to talk about the function as object, thus to say the function itself as element of $$\Lambda ^k V.$$ We derived the coefficients in our proofs by using the smooth k-form itself. We set the coefficients as...