Question

Sum of all elements in skew symmertic matrix is always 0?

Answer 1

The elements on the diagonal of a skew-symmetric matrix are zero, and therefore also its trace. If is a skew-symmetric matrix with real entries, i.e., if , then . If is a real skew-symmetric matrix and is a real eigenvalue, then . If is a real skew-symmetric matrix, then is invertible, where is the identity matrix.