[Octave-bug-tracker] [bug #34878] eigenvalue problems

[kuo-wei]

URL:
  <http://savannah.gnu.org/bugs/?34878>

                 Summary: eigenvalue problems
                 Project: GNU Octave
            Submitted by: muslim
            Submitted on: Tue 22 Nov 2011 01:00:27 PM GMT
                Category: Libraries
                Severity: 3 - Normal
                Priority: 5 - Normal
              Item Group: Incorrect Result
                  Status: None
             Assigned to: None
         Originator Name: muslim
        Originator Email: 
             Open/Closed: Open
         Discussion Lock: Any
                 Release: 3.2.4
        Operating System: GNU/Linux

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Details:


N=69;
F=fft(eye(N))/sqrt(N);
T=diag([0:floor(N/2),-floor(N/2):-1])*sqrt(2*pi/N);
A=T;
B=real(A-1i*conj(F)*A*F-F*F*A*F*F+1i*F*A*conj(F));
[v,d]=eig(B);
[a,b]=sort(diag(d));
v=v(:,b);
figure
plot(real(a),imag(a),'o');


Consider the above code, there are several problems
1. Executing this code many times(about 5~10) will generate two kinds of image
results!
2. take a look at diag(d), the eigenvalue of B, there are no zero on the
diagonal, but the null(B) is not empty, this is very strange.
3. Execute rank(v) and rank([v,F*v]) now, the answer will be 57 and 56, how
can it be possible?




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