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Scilab Help >> Linear Algebra > Matrix Pencil > quaskro


quasi-Kronecker form


[Q, Z, Qd, Zd, numbeps, numbeta] = quaskro(F)
[Q, Z, Qd, Zd, numbeps, numbeta] = quaskro(E,A)
[Q, Z, Qd, Zd, numbeps, numbeta] = quaskro(F,tol)
[Q, Z, Qd, Zd, numbeps, numbeta] = quaskro(E,A,tol)



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
  • schur — [ordered] Schur decomposition of matrix and pencils
  • spec — eigenvalues of matrices and pencils
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