Scilab Website | Contribute with GitLab | Mailing list archives | ATOMS toolboxes
Scilab Online Help
5.5.2 - Français

Change language to:
English - 日本語 - Português - Русский

Please note that the recommended version of Scilab is 2024.1.0. This page might be outdated.
See the recommended documentation of this function

Aide de Scilab >> Algèbre Lineaire > Matrice compagnon > quaskro


quasi-Kronecker form

Calling Sequence




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


two real matrices of same dimensions


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


two square orthogonal matrices


two vectors of integers


vector of integers


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. This function is obsolete.
  • gspec — valeurs propres d'un faisceau de matrices (obsolete)
Report an issue
<< penlaur Matrice compagnon randpencil >>

Copyright (c) 2022-2024 (Dassault Systèmes)
Copyright (c) 2017-2022 (ESI Group)
Copyright (c) 2011-2017 (Scilab Enterprises)
Copyright (c) 1989-2012 (INRIA)
Copyright (c) 1989-2007 (ENPC)
with contributors
Last updated:
Wed Apr 01 10:21:39 CEST 2015