ON NONNEGATIVE INVERSE EIGENVALUES PROBLEMS

Inverse eigenvalue problems constitute an important subclass of inverse problems that arise in the context of mathematical modelling and parameter identification.

The inverse eigenvalue problem for nonnegative matrices has a very simple formulation: given a list L = (λ1, λ2, . . . , λn) of complex numbers, find necessary and sufficient conditions for the existence of an n-square nonnegative matrix A with spectrum L. This problem is a very difficult one and it remains unsolved for any positive integer n.

In this work, we will reconstruct the nonnegative matrices induced by; Lowey and London for n=3, Reams for n=4 ,5 , Laffey and Meehan for n=5 ; by using Newton’s identities defined in linear algebra by Dan Kalman. Also, we use Newton’s identities to construct the non negative matrices for n=6,7,8…