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## A note on the symmetric recursive inverse eigenvalue problem

 Source file is available as : Postscript Document

Author(s) : Raphael Loewy , Volker Mehrmann

Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 737-2002

MSC 2000

15A18 Eigenvalues, singular values, and eigenvectors
15A29 Inverse problems

Abstract :
In a recent paper by Arav et al, SIAM J. Matrix Anal. and Appl., 22:392--412, 2000 the recursive inverse eigenvalue problem for matrices was introduced. In this paper we examine an open problem on the existence of symmetric positive semidefinite solutions that was posed there. We first give several counterexamples for the general case and then characterize under which further assumptions the conjecture is valid.

Keywords : recursive inverse eigenvalue problem, positive semidefinite solution