TY - JOUR
T1 - On a strong form of a conjecture of Boyle and Handelman
AU - Goldberger, Assaf
AU - Neumann, Michael
PY - 2002/8
Y1 - 2002/8
N2 - Let (equation presented). In this paper it is shown that if λ1, . . . , λn are complex numbers such that λ1 = λ2 = . . . = λr > 0 and 0 ≤ (equation presented) for 1 ≤ k ≤ m := n - r, then (equation presented) Moreover, if r ≥ m, then (*) holds for all λ ≥ λ1, while if r < m, but r is close to m, and n is large, one can lower the constant of 6.75 in the inequality (*). The inequality (*) is inspired by, and related to, a conjecture of Boyle and Handelman on the nonzero spectrum of a nonnegative matrix.
AB - Let (equation presented). In this paper it is shown that if λ1, . . . , λn are complex numbers such that λ1 = λ2 = . . . = λr > 0 and 0 ≤ (equation presented) for 1 ≤ k ≤ m := n - r, then (equation presented) Moreover, if r ≥ m, then (*) holds for all λ ≥ λ1, while if r < m, but r is close to m, and n is large, one can lower the constant of 6.75 in the inequality (*). The inequality (*) is inspired by, and related to, a conjecture of Boyle and Handelman on the nonzero spectrum of a nonnegative matrix.
KW - Inverse eigenvalue problem
KW - M-matrices
KW - Nonnegative matrices
UR - http://www.scopus.com/inward/record.url?scp=3042820498&partnerID=8YFLogxK
U2 - 10.13001/1081-3810.1082
DO - 10.13001/1081-3810.1082
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AN - SCOPUS:3042820498
SN - 1081-3810
VL - 9
SP - 138
EP - 149
JO - Electronic Journal of Linear Algebra
JF - Electronic Journal of Linear Algebra
ER -