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See the recommended documentation of this function

Scilab help >> Linear Algebra > projspec

# projspec

spectral operators

### Calling Sequence

[S,P,D,i]=projspec(A)

### Arguments

A

square matrix

S, P, D

square matrices

i

integer (index of the zero eigenvalue of A).

### Description

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.

### Examples

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 — resolvent (cofactor method)

F. D.; ;