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 | References | Similar Articles | Additional Information

Abstract: We show that there exist real numbers that occur as the eigenvalues of an entry-wise nonnegative -by- matrix but do not occur as the eigenvalues of a symmetric nonnegative -by- 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

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