projspec - spectral operators
Spectral characteristics of A at 0.
S = reduced resolvent at 0 ( S = -Drazin_inverse( A )).
P = spectral projection at 0.
D = nilpotent operator at 0.
index = index of the 0 eigenvalue.
One has (s*eye()-A)^(-1) = D^(i-1)/s^i +... + D/s^2 + P/s - S - s*S^2 -... around the singularity s=0.
deff('j=jdrn(n)','j=zeros(n,n);for k=1:n-1;j(k,k+1)=1;end')
A=sysdiag(jdrn(3),jdrn(2),rand(2,2));X=rand(7,7);
A=X*A*inv(X);
[S,P,D,index]=projspec(A);
index //size of J-block
trace(P) //sum of dimensions of J-blocks
A*S-(eye()-P)
norm(D^index,1)
coff ,
F. D.; ;