How do i find eigen vector corresponding to imaginery eigen value

[V, D] = eig(A)

The eigenvectors in V correspond to eigenvalues that can be real or complex. However, I am interested in finding the eigenvectors that correspond specifically to purely imaginary eigenvalues. Is there a way to achieve this?T

Answer 1

[Gayatri]

Hi Lokesh,

You can use 'imag' function to find the eigenvectors that correspond specifically to purely imaginary eigenvalues.

A = rand(5);
[V,D] = eig(A,'vector');
hasComplexPart = imag(D)~=0;

D = D(hasComplexPart)

D = 
  -0.3124 + 0.2799i
  -0.3124 - 0.2799i

V = V(:,hasComplexPart)

V = 
  -0.0928 + 0.4772i  -0.0928 - 0.4772i
  -0.3821 - 0.1667i  -0.3821 + 0.1667i
   0.2583 + 0.0526i   0.2583 - 0.0526i
   0.6583 + 0.0000i   0.6583 + 0.0000i
  -0.2326 - 0.1813i  -0.2326 + 0.1813i

Please refer the below documentation for 'imag' function: https://www.mathworks.com/help/symbolic/sym.imag.html

[Lokesh]

this works, thanks