In Matlab 6, there exists a command to generate a real Schur form, wheras another
transforms a real Schur form into a complex one. There do not exist commands to
prescribe the order in which the eigenvalues appear on the diagonal of the upper
(quasi-) triangular factor T.
For the complex case, a routine is sketched in Golub and Van Loan (1996), that orders the diagonal of T according to their distance to a
target value. In the reference below, we give a Matlab routine to sort real Schur forms
in Matlab. It is based on a block-swapping procedure by Bai and Demmel (1993).
Sorting real Schur forms, both partially and completely, has important applications in the
computation of real invariant subspaces.
- J.H. Brandts
- Matlab code for sorted real Schur forms
- Numerical Linear Algebra with Applications 9(3):249-261 (2002)