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


shuffle algorithm

Calling Sequence

[Ws,Fs1]=rowshuff(Fs, [alfa])



square real pencil Fs = s*E-A


polynomial matrix


square real pencil F1s = s*E1 -A1 with E1 non-singular


real number (alfa = 0 is the default value)


Shuffle algorithm: Given the pencil Fs=s*E-A, returns Ws=W(s) (square polynomial matrix) such that:

Fs1 = s*E1-A1 = W(s)*(s*E-A) is a pencil with non singular E1 matrix.

This is possible iff the pencil Fs = s*E-A is regular (i.e. invertible). The degree of Ws is equal to the index of the pencil.

The poles at infinity of Fs are put to alfa and the zeros of Ws are at alfa.

Note that (s*E-A)^-1 = (s*E1-A1)^-1 * W(s) = (W(s)*(s*E-A))^-1 *W(s)


F=rand(5,5)*F*rand(5,5);   // 5 x 5 regular pencil with 3 evals at 1,2,3
svd(E1)           //E1 non singular

See Also

  • pencan — canonical form of matrix pencil
  • glever — inverse d'un faisceau de matrices
  • penlaur — Laurent coefficients of matrix pencil
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Last updated:
Wed Apr 01 10:21:39 CEST 2015