pencan

pencan — canonical form of matrix pencil

Calling sequence

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

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

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]



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($-2:$,$-2:$))

F. D.; ;