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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The real and the symmetric nonnegative
inverse eigenvalue problems are different


Authors: Charles R. Johnson, Thomas J. Laffey and Raphael Loewy
Journal: Proc. Amer. Math. Soc. 124 (1996), 3647-3651
MSC (1991): Primary 15A18, 15A48
MathSciNet review: 1350951
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Abstract: We show that there exist real numbers $\lambda _1,\lambda _2,\dotsc ,\lambda _n$ that occur as the eigenvalues of an entry-wise nonnegative $n$-by-$n$ matrix but do not occur as the eigenvalues of a symmetric nonnegative $n$-by-$n$ matrix. This solves a problem posed by Boyle and Handelman, Hershkowitz, and others. In the process, recent work by Boyle and Handelman that solves the nonnegative inverse eigenvalue problem by appending 0's to given spectral data is refined.


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Additional Information

Charles R. Johnson
Affiliation: Department of Mathematics, College of William and Mary, Williamsburg, Virginia 23185
Email: crjohnso@cs.wm.edu

Thomas J. Laffey
Affiliation: Department of Mathematics, University College Belfield, Dublin 4, Ireland
Email: laffey@acadamh.ucd.ie

Raphael Loewy
Affiliation: Department of Mathematics, Technion-Israel Institute of Technology, Haifa 32000, Israel
Email: loewy@techunix.technion.ac.il

DOI: http://dx.doi.org/10.1090/S0002-9939-96-03587-3
PII: S 0002-9939(96)03587-3
Received by editor(s): June 9, 1994
Received by editor(s) in revised form: June 20, 1995
Additional Notes: The first and third authors’ research was supported by grant No.\ 90-00471 from the United States-Israel Binational Science Foundation, Jerusalem, Israel.
The work of the first author was supported in part by National Science Foundation grant DMS92-00899 and Office of Naval Research contract N00014-90-J-1739.
Communicated by: Lance W. Small
Article copyright: © Copyright 1996 American Mathematical Society