Summary: It is shown, how the study of the perturbed multiplication operator by a matrix polynomial in the space \(L_ 2(\mathbb{R},\mathbb{C}^ n)\) can be reduced to the study of the perturbed multiplication operator by the independent variable in the space \(L_ 2(\mathbb{R},\omega,\mathbb{C}^ n)\) with weight \(\omega\), fulfilling the Muckenhoupt condition.