Advanced Linear Algebra, Lecture 3.2: Symmetric and skew-symmetric multilinear forms

[@mengzheyan4129]

Can you explain why the last one be a skew-symmetric?

[@SilverlightLantern]

If you apply a transposition to a permutation, its sign will switch; this is true for each permutation pi (but also you'll get all the permutations back since you're ranging over S_n), so what you end up with if you apply a transposition tau to f is just the negative version of f.