Matrix quadratic equations column/row reduced factorizations and an inertia theorem for matrix polynomials

• Autorzy: Irina Karelin , Leonid Lerer
• Języki publikacji: EN

Abstrakty

EN

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 . 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.

Słowa kluczowe

EN

column (row) reduced polynomials; extremal solutions; inertia; matrix quadratic equations; algebraic Riccati equation; factorization; Bezoutians

• Wydawca: University of Zielona Gora Press
• Czasopismo: International Journal of Applied Mathematics and Computer Science
• Rocznik: 2001
• Tom: 11
• Numer: 6
• Strony: 1285-1310

Daty

wydano

2001

Twórcy

autor

Irina Karelin

• Department of Mathematics, Technion-Israel Institute of Technology, Haifa 32000, Israel

autor

Leonid Lerer

• Department of Mathematics, Technion-Israel Institute of Technology, Haifa 32000, Israel

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