TY - GEN A1 - Karelin, Irina A1 - Lerer, Leonid A2 - Curtain, Ruth - ed. A2 - Kaashoek, Rien - ed. PB - Zielona Góra: Uniwersytet Zielonogórski N2 - 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. N2 - 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. L1 - http://www.zbc.uz.zgora.pl/Content/58814/AMCS_2001_11_6_5.pdf L2 - http://www.zbc.uz.zgora.pl/Content/58814 KW - matrix quadratic equations KW - Bezoutians KW - inertia KW - column (row) reduced polynomials KW - factorization KW - algebraic Riccati equation KW - extremal solutions T1 - Matrix quadratic equations, column/row reduced factorizations and an inertia theorem for matrix polynomials UR - http://www.zbc.uz.zgora.pl/dlibra/docmetadata?id=58814 ER -