Matrix quadratic equations column/row reduced factorizations and an inertia theorem for matrix polynomials
Irina Karelin, Leonid Lerer (2001)
International Journal of Applied Mathematics and Computer Science
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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 (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. In particular, it is shown that extremal solutions of such equations correspond to spectral factorizations of...