Suppose I have a skew-symmetric tridiagonal matrix of the from \begin{equation} M = \begin{pmatrix}0 & \lambda_1 & 0 & 0 & 0 &\cdots\\ -\lambda_1 & 0 &\lambda_2 & 0 &0 & \cdots\\ 0 & -\lambda_2 & 0 & \lambda_3 & 0 & \cdots\\ 0 & 0 & -\lambda_3 & 0 & \lambda_4 & \cdots\\ \vdots & \vdots & \vdots & \vdots & \vdots & \ddots\end{pmatrix} \end{equation} with $\lambda_i \in \mathbb{R}, \ge0$ and $i\in [1,...,N]$. In my case, such a matrix is the result of performing real Schur decomposition via scipy.linalg.schur in python (for some reason it does not return them ordered).
The question:
Is there a way to come up with a matrix $\Lambda$ such that $\Lambda M \Lambda^T$ is again skew-symmetric tridiagonal but with $\lambda$s ordered (say smallest at top left)?