The real and the symmetric nonnegative inverse eigenvalue problems are different
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- by Charles R. Johnson, Thomas J. Laffey and Raphael Loewy PDF
- Proc. Amer. Math. Soc. 124 (1996), 3647-3651 Request permission
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.References
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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
- 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
- © Copyright 1996 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 124 (1996), 3647-3651
- MSC (1991): Primary 15A18, 15A48
- DOI: https://doi.org/10.1090/S0002-9939-96-03587-3
- MathSciNet review: 1350951