Quadratic matrix equations occur in a variety of applications. In this paper we introduce new permutationally invariant functions of two solvents of the n £ n quadratic matrix equation X2 ¡ L1X ¡ L0 = 0, playing the role of the two elementary symmetric functions of the two roots of a quadratic scalar equation. Our results rely on the connection existing between the QME and the theory of linear second order di®erence equations with noncommutative coe±cients. An application of our results to a simple physical problem is brie°y discussed.

Jivulescu, M.A., Napoli, A., Messina, A. (2008). Elementary symmetric functions of two solvents of a quadratic matrix equations. REPORTS ON MATHEMATICAL PHYSICS, 62(3), 369-387 [10.1016/S0034-4877(08)80031-6].

Elementary symmetric functions of two solvents of a quadratic matrix equations

NAPOLI, Anna;MESSINA, Antonino
2008-01-01

Abstract

Quadratic matrix equations occur in a variety of applications. In this paper we introduce new permutationally invariant functions of two solvents of the n £ n quadratic matrix equation X2 ¡ L1X ¡ L0 = 0, playing the role of the two elementary symmetric functions of the two roots of a quadratic scalar equation. Our results rely on the connection existing between the QME and the theory of linear second order di®erence equations with noncommutative coe±cients. An application of our results to a simple physical problem is brie°y discussed.
2008
Jivulescu, M.A., Napoli, A., Messina, A. (2008). Elementary symmetric functions of two solvents of a quadratic matrix equations. REPORTS ON MATHEMATICAL PHYSICS, 62(3), 369-387 [10.1016/S0034-4877(08)80031-6].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10447/59339
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