pencan

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