MATLAB: To get dominant eigen vector

eigen valueseigen vector

In Matlab/Octave, [A B] = eig(C) returns a matrix of eigen vectors and a diagonal matrix of eigen values of C. Even though the values may be theoretically real, these are given to be complex with very low imaginary values. Due to this, the eigen values are not put in a decreasing order. Hence to find the eigen vectors corresponding to dominant eigen values, some calculations are required, which take up processing time in a big loop. Is there a remedy to this to find dominant eigen vectors?

Best Answer

[U,S,V]=svd(C) gives you the singular value decomposition of C. i.e., C=U*S*V'

where the singular values S are in decreasing order. Therefore, the most dominant eigenvector is U(:,1), for example.

Related Solutions

MATLAB: Does adding a negligible perturbation to a matrix change the eigenvectors as returned by the EIG function in MATLAB

Eigenvectors of matrices with multiple eigenvalues are not unique, or may not even exist. The first matrix C in this case is the identity matrix, I, which is an extreme case for nonuniqueness of eigenvectors. All the eigenvalues are equal to 1, so it has maximum multiplicity. Any vector, v, is an eigenvector, that is

 I*v = 1*v

MATLAB happens to return the most natural choice for the eigenvector matrix, namely another identity matrix, but it could return any other matrix. The second matrix also has 1 as an eigenvalue of full multiplicity, but it does not have a full set of eigenvectors. Its Jordan canonical form is not diagonal.

This would have be true for any perturbation added to the original matrix and not just a small perturbation that looks like roundoff error.

The MATLAB statement,

[V,D] = eig(A)

will return matrices V and D so that A*V is close to V*D. As in the case of the perturbed matrix C1, it cannot return a non-singular or well conditioned eigenvector matrix V, if a full set of eigenvectors does not exist.

MATLAB: Generating Block Matrix Dynamically

This example show how to use blkdiag to create such a matrix

M = [0.7071    0.7071
     0.7071    0.7071];
 
n = 4;
M_cell = repmat({M}, 1, n/2);
M_out = blkdiag(M_cell{:})

Result

M_out =
    0.7071    0.7071         0         0
    0.7071    0.7071         0         0
         0         0    0.7071    0.7071
         0         0    0.7071    0.7071

You can avoid for-loop in your code.

Best Answer

Related Solutions

MATLAB: Does adding a negligible perturbation to a matrix change the eigenvectors as returned by the EIG function in MATLAB

MATLAB: Generating Block Matrix Dynamically

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