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Thank you! It is really interesting approach and works perfectly well for the uploaded case. But the real problem is that I can not  symbolically calculate the eigensystem (due to the  huge dimensions of the matrices in the actual problem I use...
Thank you, my mistake, in that particular case it is. But i don't think that it was going to mess with eigenvalue calculations, because you do not engage in inverted matrix consideration when obtaining the eigenvalues (or does the internal algorithm...