The following matrix is not hermitian.
A = [0 2; -2 0]
A =
0 2 -2 0
It has an eigenvalue decomposition with a unitary matrix of eigenvectors, though, so it is normal.
[V,D] = eig(A);
norm( V'*V - eye(2) )
ans =
2.2204e-16
The eigenvalues are pure imaginary.
lambda = diag(D)
lambda =
0.0000e+00 + 2.0000e+00i 0.0000e+00 - 2.0000e+00i
The singular values are the complex magnitudes of the eigenvalues.
svd(A)
ans =
2 2