Elementary symmetric functions of two solvents of a quadratic matrix equations
- Autori: Jivulescu, M.; Napoli, A.; Messina, A.
- Anno di pubblicazione: 2008
- Tipologia: Articolo in rivista (Articolo in rivista)
- Parole Chiave: quadratic matrix equation; solvent; difference equation; symmetric functions
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.