Solutions of the Unilateral Quadratic Matrix Equation in the Case of Complex Eigenvalues of the Corresponding Matrix Pencil

摘要

The algorithm for constructing solutions of the unilateral quadratic matrix equation in the case of complex eigenvalues of the corresponding matrix pencil is proposed. Relations are given which can be regarded as analogues of the corresponding equalities for the scalar quadratic equation, which are content of Vieta theorem. As an application, the problem of introducing clarity into the model parameters, using the experimentally obtained eigenvalues of this system, is considered.