is diagonal of skew symmetric is zero
All main diagonal entries of a skew-symmetric matrix must be zero, so the trace is zero. If A = (aij) is skew-symmetric, aij = âaji; hence aii = 0. 3x3 skew symmetric matrices can be used to represent cross products as matrix multiplications.ore generally, every complex skew-symmetric matrix can be written in the form A = U Ï U T where U is unitary and Ï has the block-diagonal form given above with complex Î» k. This is an example of the Youla decomposition of a complex square matrix.