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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

Eigenvalue problem, inverse eigenvalue problem, Newton’s identities, nonnegative matrix, spectrum.

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MUHAMMED, D. M., OLGUN, N., & FATTAH HAMA, M. (2019). ON NONNEGATIVE INVERSE EIGENVALUES PROBLEMS. Asian Journal of Mathematics and Computer Research, 26(3), 155-175. Retrieved from https://www.ikprress.org/index.php/AJOMCOR/article/view/4744
Original Research Article


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