1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
|
projspec Scilab Group Scilab Function projspec
NAME
projspec - spectral operators
CALLING SEQUENCE
[S,P,D,i]=projspec(A)
PARAMETERS
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.
EXAMPLE
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)
SEE ALSO
coff
AUTHOR
F. D.
|
