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. 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.
Lingua originaleEnglish
pagine (da-a)369-387
Numero di pagine19
RivistaReports on Mathematical Physics
Volume62
Stato di pubblicazionePublished - 2008

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Quadratic Matrix Equation
Elementary Symmetric Functions
Roots
Scalar
Invariant
scalars

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cita questo

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title = "Elementary symmetric functions of two solvents of a quadratic matrix equations",
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{\circledR}erence equations with noncommutative coe±cients. An application of our results to a simple physical problem is brie°y discussed.",
keywords = "quadratic matrix equation; solvent; difference equation; symmetric functions",
author = "Antonino Messina and Anna Napoli and Jivulescu",
year = "2008",
language = "English",
volume = "62",
pages = "369--387",
journal = "Reports on Mathematical Physics",
issn = "0034-4877",
publisher = "Elsevier Limited",

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TY - JOUR

T1 - Elementary symmetric functions of two solvents of a quadratic matrix equations

AU - Messina, Antonino

AU - Napoli, Anna

AU - Jivulescu, null

PY - 2008

Y1 - 2008

N2 - 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.

AB - 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.

KW - quadratic matrix equation; solvent; difference equation; symmetric functions

UR - http://hdl.handle.net/10447/59339

M3 - Article

VL - 62

SP - 369

EP - 387

JO - Reports on Mathematical Physics

JF - Reports on Mathematical Physics

SN - 0034-4877

ER -