eig return complex values
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Hello,
I'm trying to find the eigenvalues and eigenvectors of an invertible matrix. The eig function returns me complex values.
But the matrix is invertible: I invert it on Pascal.
How to explain and especially how to solve this problem please?
The matrix I am trying to invert is the inv(C)*A matrix, from the attached files.
Thanks,
Michael
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Réponse acceptée
Torsten
le 22 Jan 2022
Modifié(e) : Torsten
le 22 Jan 2022
Use
E = eig(A,C)
instead of
E = eig(inv(C)*A)
or
E = eig(C\A)
4 commentaires
Torsten
le 22 Jan 2022
Modifié(e) : Torsten
le 22 Jan 2022
Although negligible, eig(A,C) produces no imaginary parts.
E = eig(A,C) solves for the lambda-values that satisfy
A*x = lambda*C*x (*)
for a vector x~=0.
If C is invertible, these are the eigenvalues of inv(C)*A (as you can see by multiplying (*) with
inv(C) ).
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Matt J
le 22 Jan 2022
Modifié(e) : Matt J
le 22 Jan 2022
It turns out that B=C\A does have real eigenvalues in this particular case, but floating point errors approximations produce a small imaginary part that can be ignored.
load matrices
E=eig(C\A);
I=norm(imag(E))/norm(real(E))
So just discard the imaginary values,
E=real(E);
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