pencan

canonical form of matrix pencil

Calling Sequence

[Q,M,i1]=pencan(Fs)
[Q,M,i1]=pencan(E,A)

Arguments

:Fs a regular pencil s*E-A : :E,A two real square matrices : :Q,M two non-singular real matrices : :i1 integer :

Description

Given the regular pencil Fs=s*E-A, pencan returns matrices Q and M such than M*(s*E-A)*Q is in “canonical” form.

M*E*Q is a block matrix

[I,0;
 0,N]

with N nilpotent and i1 = size of the I matrix above.

M*A*Q is a block matrix:

[Ar,0;
 0,I]

Examples

F=`randpencil`_([],[1,2],[1,2,3],[]);
F=`rand`_(6,6)*F*`rand`_(6,6);
[Q,M,i1]=pencan(F);
W=`clean`_(M*F*Q)
`roots`_(`det`_(W(1:i1,1:i1)))
`det`_(W($-2:$,$-2:$))

See Also

• glever inverse of matrix pencil
• penlaur Laurent coefficients of matrix pencil
• rowshuff shuffle algorithm