I am looking for a publicly-available software package (preferably in Python, but I'll take what I can get) capable of performing a decomposition of a real $n\times n$ skew-symmetric (sometimes called anti-symmetric) matrix $\textbf{A} = - \textbf{A}^T$. I have seen this decomposition referred to as the Youla decomposition, for example, in this Wikipedia article. I don't want to assume that this terminology is well-known, so I will describe the decomposition here.
The decomposition consists in finding an orthogonal matrix $\textbf{Q}$ such that $$ \textbf{A} = \textbf{Q} \Sigma \textbf{Q}^T \,,$$
and $\Sigma$ is of the form: \begin{equation}\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_r\\ -\lambda_r & 0\end{matrix} \\ & & & & \begin{matrix}0 \\ & \ddots \\ & & 0 \end{matrix} \end{bmatrix} \,. \end{equation} for real $\lambda_k$.