A Sylvester equation is a matrix equation of the form
 |
where 
is 
,
is 
,
is 
,
and the 
matrix 
is to be determined. The equation has a unique solution for every 
if and only if no eigenvalue
of 
is the negative of an eigenvalue of 
, or equivalently, if the matrix
spectra of 
and 
are disjoint. The Bartels-Stewart algorithm solves the equation after applying a
Schur decomposition to 
and 
.
[F4]." Commun. ACM 15, 820-826, 1972.