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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
  • OA Link:


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.