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Efficient
realization of nonzero spectra by polynomial matrices
Nathan McNew and Nicholas Ormes
Vol. 8 (2015), No. 1, 1–24
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Abstract |
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A theorem of Boyle and Handelman gives necessary and sufficient conditions for an -tuple of nonzero complex numbers to be the nonzero spectrum of some matrix with nonnegative entries, but is not constructive and puts no bound on the necessary dimension of the matrix. Working with polynomial matrices, we constructively reprove this theorem in a special case, with a bound on the size of the polynomial matrix required to realize a given polynomial. |
Keywords
nonnegative matrices, eigenvalues, power series,
nonnegative inverse eigenvalue problem
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Mathematical Subject Classification 2010
Primary: 15A18, 15B48, 05C50
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Milestones
Received: 5 September 2011
Revised: 1 February 2014
Accepted: 5 March 2014
Published: 10 December 2014
Communicated by Kenneth S. Berenhaut
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Authors |
| Nathan McNew | |
| Department of Mathematics Dartmouth College 6188 Kemeny Hall Hanover, NH 03755 United States |
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| Nicholas Ormes | |
| Department of Mathematics University of Denver 2280 South Vine Street Denver, CO 80208 United States |
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