eig return complex values

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Michael cohen
Michael cohen 2022-1-22
评论： Matt J 2022-1-23
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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Michael cohen
Michael cohen 2022-1-22
编辑：Michael cohen 2022-1-22
Thank you, but in fact it is the matrix_invC.A.mat that I try to diagonalize :)
Matt J
Matt J 2022-1-22
编辑：Matt J 2022-1-22
That matrix is not symmetric, so there is no reason to think it will have real eigenvalues.

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采纳的回答

Torsten
Torsten 2022-1-22
编辑：Torsten 2022-1-22
Use
E = eig(A,C)
instead of
E = eig(inv(C)*A)
or
E = eig(C\A)
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Torsten
Torsten 2022-1-22
编辑：Torsten 2022-1-22
@Matt J
Although negligible, eig(A,C) produces no imaginary parts.
@Michael cohen
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) ).
Michael cohen
Michael cohen 2022-1-23
Wouah, thank you very much. It’s very clear and allow us to solve our problem 🙏

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Matt J
Matt J 2022-1-22
编辑：Matt J 2022-1-22
Ran in:
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))
I = 3.3264e-18
So just discard the imaginary values,
E=real(E);
  2 个评论
Michael cohen
Michael cohen 2022-1-23
Thank you very much @Matt J for all those explanations !
Matt J
Matt J 2022-1-23
You 're welcome but please Accept-click one of the answers.

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