1996
DOI: 10.1080/03081089608818485
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An inequality for nonnegative matrices and the inverse eigenvalue problem

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Cited by 64 publications
(35 citation statements)
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“…Authors have studied the case where the ntuple is comprised of real numbers [Bor95,Cia68,Fri78,Kel71,Per53,Sal72,Sou83,Sul49], the case where the matrices under consideration are symmetric [Fie74,JLL96], and the general problem [Joh81,LM99,LL79,Rea94,Rea96,Wuw97]. Various necessary conditions and sufficient conditions have been provided, but a complete characterization is known for real n-tuples only for n ≤ 4 [ Kel71,Sul49] and for complex n-tuples only for n ≤ 3 [LL79].…”
Section: Introductionmentioning
confidence: 99%
“…Authors have studied the case where the ntuple is comprised of real numbers [Bor95,Cia68,Fri78,Kel71,Per53,Sal72,Sou83,Sul49], the case where the matrices under consideration are symmetric [Fie74,JLL96], and the general problem [Joh81,LM99,LL79,Rea94,Rea96,Wuw97]. Various necessary conditions and sufficient conditions have been provided, but a complete characterization is known for real n-tuples only for n ≤ 4 [ Kel71,Sul49] and for complex n-tuples only for n ≤ 3 [LL79].…”
Section: Introductionmentioning
confidence: 99%
“…pdf). Readers also may refer to [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26] for some previous results. In some articles, some necessary conditions and sufficient conditions for the three problems above have been given under some small dimension or special cases [7].…”
Section: Problem 3 (Sniep)mentioning
confidence: 99%
“…A short list of references giving various necessary or sufficient conditions includesBarrett and Johnson (1984), Boyle and Handelman (1991), Friedland (1978), Friedland and Melkman (1979), Loewy and London (1978), de Oliveira (1983), and Reams (1996). The difficulty is that the necessary condition is usually too general and the sufficient condition too specific.…”
mentioning
confidence: 99%
“…In the general case, when the possible spectrum Λ is a set of complex numbers, the problem has only been solved for n = 3 by Loewy and London [11]. The complex cases n = 4 and n = 5 have been solved for matrices of trace zero by Reams [17] and Laffey and Meehan [10], respectively. Sufficient conditions or realizability criteria for the existence of a nonnegative matrix with a given real spectrum have been obtained in [25,14,15,18,8,1,19,22] (see [3, §2.1] and references therein for a comprehensive survey).…”
Section: Introductionmentioning
confidence: 99%