Sylvester Equations VI

The following equations define the Sylvester matrix equation:

or

where op(A) is A or the conjugate transpose of A, op(B) is B or the conjugate transpose of B, and a is a scaling factor to avoid overflow in X.

The Sylvester matrix equation has a unique solution if and only if λ ± β ≠ 0, where λ and β are the eigenvalues of A and B, respectively, and the sign (+ or –) depends on the equation you want to solve. When the solution of the Sylvester matrix equation is not unique, this VI sets perturbed to TRUE and might not return the correct solution.