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
5 个评论
Matt J
2022-1-22
Invertible matrices can have complex eigenvalues. That in itself is not a sign of a problem.
Michael cohen
2022-1-22
A diagonalizable matrix can also be invertible with complex eigenvalues. A simple example is C=1i*eye(N).
In any case, I do not see the complex eigenvalues for the matrix you've provided.
load(websave('t','https://www.mathworks.com/matlabcentral/answers/uploaded_files/869735/matrix_C.mat'))
isreal(eig(C))
Michael cohen
2022-1-22
编辑：Michael cohen
2022-1-22
采纳的回答
Use
E = eig(A,C)
instead of
E = eig(inv(C)*A)
or
E = eig(C\A)
4 个评论
Michael cohen
2022-1-22
Moreover, I don't have quite the same results when comparing the real part of the first method eig(C\A) and the one you propose,
There is essentially no difference in the results of the two methods:
load matrices;
E0=sort( real(eig(C\A)) );
E=sort( eig(A,C) );
I=1:248;
plot(I,E0,'x', I,E,'--'); legend('eig(C\A)','eig(A,C)','interpreter','none')
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) ).
Michael cohen
2022-1-23
更多回答（1 个）
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);
2 个评论
Michael cohen
2022-1-23
Matt J
2022-1-23
You 're welcome but please Accept-click one of the answers.
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