$A = \begin{pmatrix} 2 & 1+i \\ 1-i & 3 \end{pmatrix}$ (Hermitian)

$A = \begin{pmatrix} 0 & 1 \\ -1 & 0 \end{pmatrix}$ (skew-symmetric)

$A = \begin{pmatrix} 1 & 2 \\ 0 & 3 \end{pmatrix}$ (upper triangular)

$A = \begin{pmatrix} \cos\theta & -\sin\theta \\ \sin\theta & \cos\theta \end{pmatrix}$ (orthogonal)