Elementary symmetric functions of two solvents of a quadratic matrix equation

Details Elementary symmetric functions of two solvents of a quadratic matrix equation Elementary symmetric functions of two solvents of a quadratic matrix equation

2008-04-18

arxiv.org/abs/0804.2978v1

Physics

Mathematical Physics

20 pages

Scientific paper

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.

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