Realizing suleimanova spectra via permutative matrices

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Electronic Journal of Linear Algebra, ISSN: 1081-3810, Vol: 31, Issue: 1, Page: 306-312

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Paparella, Pietro
University of Wyoming Libraries
Mathematics; Mathematics - Rings and Algebras; 15A18, 15A29, 15B99; Suleimanova spectrum; permutative matrix; real nonnegative inverse eigenvalue problem.
article description
A permutative matrix is a square matrix such that every row is a permutation of the first row. A constructive version of a result attributed to Suleĭmanova is given via permutative matrices. A well-known result is strenghthened by showing that all realizable spectra containing at most four elements can be realized by a permutative matrix or by a direct sum of permutative matrices. The paper concludes by posing a problem.