Eigenvectors of a nonsymmetric matrix.

Hello, I'm trying to find the dominant Eigenvectors of a matrix P. However, P could be non symmetric thus their are two "categories" of eigenvectors (left and right). Here I'm looking for the left dominant eigenvector of P (or the right dominant eigenvector of P').

What I don't know is, have I to use eig, or eigs function ? How to differentiate left eigenvectors from right eigenvectors ?

Thank you for your answers.

Answer 1

[Wayne King]

Below W are the left eigenvectors, use the one associate with the largest eigenvalue.

If A is your matrix

   [W,D] = eig(A.'); 
   W = conj(W)

[Collet Bastien]

I tried it, it seems to work but, I don't understand what is the purpose of conj (I checked the doc but I can't figure out why is it useful here).

Maybe can you tell me ?

Anyway, thanks for you answer.

[Collet Bastien]

When you say "left eigenvectors", is it the left eigenvectors of A, or A' ?

[Wayne King]

That's because we didn't conjugate the entries of A, we used A.'

You can omit that step if you do [W,D] = eig(A');