CODEWITHSUNDEEP
matlabmatrixeigenvector
passerby51
passerby51

Reputation: 955

Complex eigenvectors for symmetric matrix in MATLAB

I have the following code snippet, trying to compute the eigen-decomposition of a real symmetric matrix

K = 3;
n = 10;

Z = rand(n,K);
B = rand(K,K);
B = 0.5*(B+B') + 3*eye(K);
W = Z*B*Z';
if issymmetric(W) && isreal(W)
    [U,D] = eig(W)
end

This unfortunately seems to produce genuinely complex eigenvectors on MATLAB R2013a. I used to think that eig should keep everything real for real symmetric matrices. Anyone has any idea why this happens?

PS. Changing to n = 6, for example, outputs something real.

Upvotes: 1

Views: 1019

Answers (1)

Eloy
Eloy

Reputation: 21

MATLAB eig usually returns real eigenvectors when the matrix is real and symmetric. Rounding errors can make Z*B*Z' slightly unsymmetric. I don't know how issymmetric is implemented (it's a built-in function), but maybe eig doesn't use the same criterion to determine if a matrix is real and symmetric than issymmetric.

A simple way to enforce that the matrix is numerically symmetric is doing (W+W')./2. So eig((W+W')./2) should return real values and vectors.

Upvotes: 1

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