A = matrix(CDF, [[I, 1 + I ],[-1  + I, -2*I]])
Ac = A.conjugate() #complex conjugate
Act = Ac.transpose() #conjugate transpose
A
Act
# Act = -A => A is skew Hermitian
X = matrix(CDF, [[2],[I]])
Xc = X.conjugate()
Xct = Xc.transpose()
Xct*A*X