The $n\times n$ imaginary matrix $A$ satisfies $A^\top=-A$, so it is skew-symmetric. The Youla decomposition is $$A=iO\Sigma O^\top,$$ where $O$ is a real orthogonal matrix and $\Sigma$ is a real block-diagonal matrix of the form $$\Sigma = \begin{bmatrix} \begin{matrix}0 & \lambda_1 \\ -\lambda_1 & 0\end{matrix} & 0 & \cdots & 0 \\ 0 & \begin{matrix}0 & \lambda_2 \\ -\lambda_2 & 0\end{matrix} & & 0 \\ \vdots & & \ddots & \vdots \\ 0 & 0 & \cdots & \begin{matrix}0 & \lambda_{n/2}\\ -\lambda_{n/2} & 0\end{matrix} \end{bmatrix} $$ for $n$ even. If $n$ is odd a row and column of zeroes is appended.

The $n\times n$ imaginary matrix $A$ satisfies $A^\top=-A$, so it is skew-symmetric. The Youla decomposition is $$A=iO\Sigma O^\top,$$ where $O$ is a real orthogonal matrix and $\Sigma$ is a real block-diagonal matrix of the form $$\Sigma = \begin{pmatrix} \begin{matrix}0 & \lambda_1 \\ -\lambda_1 & 0\end{matrix} & 0 & \cdots & 0 \\ 0 & \begin{matrix}0 & \lambda_2 \\ -\lambda_2 & 0\end{matrix} & & 0 \\ \vdots & & \ddots & \vdots \\ 0 & 0 & \cdots & \begin{matrix}0 & \lambda_{n/2}\\ -\lambda_{n/2} & 0\end{matrix} \end{pmatrix} $$ for $n$ even. If $n$ is odd a row and column of zeroes is appended.