- #1
Maxi1995
- 14
- 0
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 someone explain me why the alternator is alternating, thus to say if I change two argument vectors in Alt, then a minus will appear, as an example
$$w(v_1,...,v_n)=- w(v_n,...,v_1)$$
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 someone explain me why the alternator is alternating, thus to say if I change two argument vectors in Alt, then a minus will appear, as an example
$$w(v_1,...,v_n)=- w(v_n,...,v_1)$$