A Note on the Symmetric Recursive Inverse Eigenvalue Problem | Zendy

Raphael Loewy | Zendy; Volker Mehrmann | Zendy

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A Note on the Symmetric Recursive Inverse Eigenvalue Problem

Author(s) -

Raphael Loewy,

Volker Mehrmann

Publication year - 2003

Publication title -

siam journal on matrix analysis and applications

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.268

H-Index - 101

eISSN - 1095-7162

pISSN - 0895-4798

DOI - 10.1137/s0895479802408839

Subject(s) - mathematics , eigenvalues and eigenvectors , counterexample , inverse , positive definite matrix , conjecture , symmetric matrix , inverse iteration , semidefinite programming , matrix (chemical analysis) , combinatorics , pure mathematics , mathematical optimization , physics , geometry , materials science , quantum mechanics , composite material

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.

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