Elementary symmetric functions of two solvents of a quadratic matrix equations

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Abstract

Quadratic matrix equations occur in a variety of applications. Inthis paper we introduce new permutationally invariant functions oftwo solvents of the n £ n quadratic matrix equation X2 ¡ L1X ¡L0 = 0, playing the role of the two elementary symmetric functionsof the two roots of a quadratic scalar equation. Our results rely onthe connection existing between the QME and the theory of linearsecond order di®erence equations with noncommutative coe±cients.An application of our results to a simple physical problem is brie°ydiscussed.
Lingua originaleEnglish
pagine (da-a)369-387
Numero di pagine19
RivistaReports on Mathematical Physics
Volume62
Stato di pubblicazionePublished - 2008

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All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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