posted on 2013-11-26, 00:00authored byShmuel Friedland
In this note we extend the necessary and sufficient conditions of Boyle-Handleman [M. Boyle and D. Handelman, The spectra of nonnegative matrices via symbolic dynamics, Ann. Math. 133 (1991), pp. 249-316] and Kim-Ormes-Roush [K.H. Kim, N.S. Ormes, and F.W. Roush, The spectra of nonnegative integer matrices via formal power series, J. Am. Math. Soc. 13 (2000), pp. 773-806] for a nonzero eigenvalue multiset of primitive matrices over R+ and Z(+), respectively, to irreducible matrices.
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Post print version of article may differ from published version. This is an electronic version of an article published in Friedland S. A note on the nonzero spectra of irreducible matrices. Linear & Multilinear Algebra. 2012;60(11-12):1235-1238.. Linear and Multilinear Algebra is available online at: http://www.informaworld.com/smpp/ DOI: 10.1080/03081087.2011.616203