6533b82efe1ef96bd12932cd
RESEARCH PRODUCT
Elementary symmetric functions of two solvents of a quadratic matrix equations
Anna NapoliAntonino MessinaMaria Anastasia JivulescuMaria Anastasia Jivulescusubject
Pure mathematicsDifferential equationquadratic matrix equationFOS: Physical sciencesStatistical and Nonlinear Physicsdifference equationMathematical Physics (math-ph)Noncommutative geometrysolventquadratic matrix equation; solvent; difference equation; symmetric functions15A24Symmetric functionMatrix (mathematics)Quadratic equationSimple (abstract algebra)symmetric functionsVariety (universal algebra)Connection (algebraic framework)Mathematical PhysicsMathematicsdescription
Quadratic matrix equations occur in a variety of applications. In this paper we introduce new permutationally invariant functions of two solvents of the n quadratic matrix equation X^2- 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 difference equations with noncommutative coefficients. An application of our results to a simple physical problem is briefly discussed.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2008-01-01 |