@misc{Karelin_Irina_Matrix, author={Karelin, Irina and Lerer, Leonid}, howpublished={online}, publisher={Zielona Góra: Uniwersytet Zielonogórski}, language={eng}, abstract={It is shown that a certain Bezout operator provides a bijective correspondence between the solutions of the matrix quadratic equation and factorizatons of a certain matrix polynomial G([lambda]) (which is a specification of a Popov-type function) into a product of row and column reduced polynomials. Special attention is paid to the symmetric case, i.e. to the Algebraic Riccati Equation.}, abstract={In particular, it is shown that extremal solutions of such equations correspond to spectral factorizations of G([lambda]). The proof of these results depends heavily on a new inertia theorem for matrix polynomials which is also one of the main results in this paper.}, type={artykuł}, title={Matrix quadratic equations, column/row reduced factorizations and an inertia theorem for matrix polynomials}, keywords={matrix quadratic equations, Bezoutians, inertia, column (row) reduced polynomials, factorization, algebraic Riccati equation, extremal solutions}, }