randpencil

random pencil

Calling Sequence

F=randpencil(eps,infi,fin,eta)

Arguments

:eps vector of integers : :infi vector of integers : :fin real vector, or monic polynomial, or vector of monic polynomial : :eta vector of integers : :F real matrix pencil F=s*E-A ( s=poly(0,’s’)) :

Description

Utility function. F=randpencil(eps,infi,fin,eta) returns a random pencil F with given Kronecker structure. The structure is given by: eps=[eps1,...,epsk]: structure of epsilon blocks (size eps1x(eps1+1),....) fin=[l1,...,ln] set of finite eigenvalues (assumed real) (possibly []) infi=[k1,...,kp] size of J-blocks at infinity ki>=1 (infi=[] if no J blocks). eta=[eta1,...,etap]: structure ofeta blocks (size eta1+1)xeta1,...)

epsi‘s should be >=0, etai‘s should be >=0, infi‘s should be >=1.

If fin is a (monic) polynomial, the finite block admits the roots of fin as eigenvalues.

If fin is a vector of polynomial, they are the finite elementary divisors of F i.e. the roots of p(i) are finite eigenvalues of F.

Examples

F=randpencil([0,1],[2],[-1,0,1],[3]);
[Q,Z,Qd,Zd,numbeps,numbeta]=`kroneck`_(F);
Qd, Zd
s=`poly`_(0,'s');
F=randpencil([],[1,2],s^3-2,[]); //regular pencil
`det`_(F)

See Also

  • kroneck Kronecker form of matrix pencil
  • pencan canonical form of matrix pencil
  • penlaur Laurent coefficients of matrix pencil

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