# schur_ordered¶

Returns block ordered complex Schur form of matrix $$\mathbf{A}$$

$\begin{split}\mathbf{TAT}^H = \mathbf{A}_s = \begin{bmatrix} A_{11} & A_{12} \\ 0 & A_{22} \end{bmatrix}\end{split}$

where $$A_{11}\in\mathbb{C}^{s\times s}$$ contains the $$s$$ stable eigenvalues of $$\mathbf{A}\in\mathbb{R}^{m\times m}$$.

param A

Matrix to decompose.

type A

np.ndarray

param ct

Continuous time system.

type ct

bool

returns

Tuple containing the Schur decomposition of $$\mathbf{A}$$, $$\mathbf{A}_s$$; the transformation $$\mathbf{T}\in\mathbb{C}^{m\times m}$$; and the number of stable eigenvalues of $$\mathbf{A}$$.

rtype

tuple

Notes

This function is a wrapper of scipy.linalg.schur imposing the settings required for this application.