scipy.linalg.solve_sylvester¶

scipy.linalg.
solve_sylvester
(a, b, q)[source]¶ Computes a solution (X) to the Sylvester equation \(AX + XB = Q\).
Parameters: a : (M, M) array_like
Leading matrix of the Sylvester equation
b : (N, N) array_like
Trailing matrix of the Sylvester equation
q : (M, N) array_like
Righthand side
Returns: x : (M, N) ndarray
The solution to the Sylvester equation.
Raises: LinAlgError
If solution was not found
Notes
Computes a solution to the Sylvester matrix equation via the Bartels Stewart algorithm. The A and B matrices first undergo Schur decompositions. The resulting matrices are used to construct an alternative Sylvester equation (
RY + YS^T = F
) where the R and S matrices are in quasitriangular form (or, when R, S or F are complex, triangular form). The simplified equation is then solved using*TRSYL
from LAPACK directly.New in version 0.11.0.