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2015 Efficient realization of nonzero spectra by polynomial matrices
Nathan McNew, Nicholas Ormes
Involve 8(1): 1-24 (2015). DOI: 10.2140/involve.2015.8.1

Abstract

A theorem of Boyle and Handelman gives necessary and sufficient conditions for an n-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.

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Nathan McNew. Nicholas Ormes. "Efficient realization of nonzero spectra by polynomial matrices." Involve 8 (1) 1 - 24, 2015. https://doi.org/10.2140/involve.2015.8.1

Information

Received: 5 September 2011; Revised: 1 February 2014; Accepted: 5 March 2014; Published: 2015
First available in Project Euclid: 22 November 2017

zbMATH: 1311.15013
MathSciNet: MR3321706
Digital Object Identifier: 10.2140/involve.2015.8.1

Subjects:
Primary: 05C50 , 15A18‎ , 15B48

Keywords: Eigenvalues , nonnegative inverse eigenvalue problem , nonnegative matrices , Power series

Rights: Copyright © 2015 Mathematical Sciences Publishers

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