A Note on the Symmetric Recursive Inverse Eigenvalue Problem
Raphael Loewy, Volker Mehrmann · SIAM Journal on Matrix Analysis and Applications · 2003
In [M. Arav et al., SIAM J. Matrix Anal. Appl., 22 (2000), pp. 392--412] 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.