quaskro

Arguments

F

real matrix pencil F=s*E-A (s=poly(0,'s'))

E,A

two real matrices of same dimensions

tol

a real number (tolerance, default value=1.d-10)

Q,Z

two square orthogonal matrices

Qd,Zd

two vectors of integers

numbeps

vector of integers

Description

Quasi-Kronecker form of matrix pencil: quaskro computes two orthogonal matrices Q, Z which put the pencil F=s*E -A into upper-triangular form:

| sE(eps)-A(eps) |        X       |      X     |
|----------------|----------------|------------|
|        O       | sE(inf)-A(inf) |      X     |
Q(sE-A)Z = |=================================|============|
|                                 |            |
|                O                | sE(r)-A(r) |

The dimensions of the blocks are given by:

eps=Qd(1) x Zd(1), inf=Qd(2) x Zd(2), r = Qd(3) x Zd(3)

The inf block contains the infinite modes of the pencil.

The f block contains the finite modes of the pencil

The structure of epsilon blocks are given by:

numbeps(1) = # of eps blocks of size 0 x 1

numbeps(2) = # of eps blocks of size 1 x 2

numbeps(3) = # of eps blocks of size 2 x 3 etc...

The complete (four blocks) Kronecker form is given by the function kroneck which calls quaskro on the (pertransposed) pencil sE(r)-A(r).

The code is taken from T. Beelen

See Also

• kroneck — Kronecker form of matrix pencil
• gschur — generalized Schur form (obsolete).
• gspec — eigenvalues of matrix pencil (obsolete)