Original sentence: An alternating form φ on a vector space V over a field K is defined (if K doesn't have characteristic 2) to be a bilinear form.In particular, if n is odd, and the underlying field is not of characteristic 2, the determinant vanishes
Edited sentence: An alternating form φ on a vector space V over a field K is defined (again we assume K does not have characteristic 2) to be a bilinear form.In particular, if n is odd, and since the underlying field is not of characteristic 2, the determinant vanishes.We assume that the the underlying field is not of characteristic 2: that is, that 1+1≠0; otherwise a skew-symmetric matrix is just the same thing as a symmetric matrix