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Existence and construction of nonnegative matrices with complex spectrum

✍ Scribed by Oscar Rojo; Ricardo L. Soto

Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
150 KB
Volume
368
Category
Article
ISSN
0024-3795

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✦ Synopsis

The following inverse spectrum problem for nonnegative matrices is considered: given a set of complex numbers Οƒ = {Ξ» 1 , Ξ» 2 , . . . , Ξ» n }, find necessary and sufficient conditions for the existence of an n Γ— n nonnegative matrix A with spectrum Οƒ . Our work is motivated by a relevant theoretical result of Guo Wuwen [Linear Algebra Appl. 266 (1997) 261, Theorem 2.1]: there exists a real parameter Ξ» 0 max 2 j n |Ξ» j | such that the problem has a solution if and only if Ξ» 1 Ξ» 0 . In particular, we discuss how to compute Ξ» 0 and the solution matrix A for certain class of matrices. A sufficient condition for the problem to have a solution is also derived.

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