How to find a complex eigenvalue of a matrix

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MM 2019-12-17

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https://ww2.mathworks.cn/matlabcentral/answers/497030-how-to-find-a-complex-eigenvalue-of-a-matrix

回答： MM 2020-2-3

采纳的回答： MM

在 MATLAB Online 中打开

I want to find the highest complex eigenvalue of a matrix A. For example:

lambda = eig(A)

I'll get:

lambda =
   2.6955 + 0.0000i
  -1.1216 + 3.9723i
  -1.1216 - 3.9723i
  -1.7535 + 0.0000i
  -0.1240 + 2.2553i
  -0.1240 - 2.2553i

When I do:

[lambda_max, index_max] = max(real(lambda))

I'll get:

  lambda_max =
    2.6955

While I would like to have

-0.1240

How can I do this?

(sometimes the imaginairy part of complex eigenvalues can be zero)

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MM 2019-12-18

在 MATLAB Online 中打开

It looks like it works when I do it like this:

   lambda_conj = [];
    for ii = 1:length(lambda)
        for jj = 1:length(lambda)
            if ii == jj
                
            elseif uniquetol(real(lambda(ii))) == uniquetol(real(lambda(jj)))
                lambda_conj = [lambda_conj; lambda(ii)];
            end
        end
    end
    lambda = lambda_conj;

but it looks like this does the same:

    lambda_conj = [];
    for ii = 1:length(lambda)
        for jj = 1:length(lambda)
            if ii == jj
                
            elseif real(lambda(ii)) == real(lambda(jj))
                lambda_conj = [lambda_conj; lambda(ii)];
            end
        end
    end
    lambda = lambda_conj;

But I think the way I used uniquetol, it doesn't really do anything. It probably only looks to that one value of lambda so it will always gave the same output as when I don't use it. I didn't test it yet but I think both methods will fail when for example the values are

-1.121600000000000 + 3.9723i

-1.121600000000001 - 3.9723i

(I don't know what the standard tolerance is, even if I say the tolerance is 0.0005. Both methods will probably still fail when the difference is as small as mentioned above)

Steven Lord 2019-12-18

I think the cplxpair function may be of interest to you in making sure the complex conjugate pairs are grouped together.

Walter Roberson 2019-12-18

在 MATLAB Online 中打开

lambda = [
   2.6955 + 0.0000i
  -1.1216 + 3.9723i
  -1.1216 - 3.9723i
  -1.7535 + 0.0000i
  -0.1240 + 2.2553i
  -0.1240 - 2.2553i];
[uniquegroups, ~, group] = uniquetol([real(lambda), abs(imag(lambda))], 'byrows', true);
groupcounts = accumarray(group, 1);
maxeigreal = max(real(uniquegroups(groupcounts>1,:)));