Matrix quadratic equations, column/row reduced factorizations and an inertia theorem for matrix polynomials - Karelin, Irina; Lerer, Leonid (Zielona Góra: Uniwersytet Zielonogórski)
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.
Keywords: matrix quadratic equations; Bezoutians; inertia; column (row) reduced polynomials; factorization; algebraic Riccati equation; extremal solutions