Abstract
The nonnegative inverse eigenvalue problem (NIEP) consists of finding necessary and sufficient conditions for the existence of a nonnegative matrix with a given list of complex numbers as its spectrum. If the matrix is required to be Leslie (doubly Leslie), the problem is called the Leslie (doubly Leslie) nonnegative eigenvalue inverse problem. In this paper, necessary and/or sufficient conditions for the existence and construction of Leslie and doubly Leslie matrices with a given spectrum are considered.
Highlights
The nonnegative inverse eigenvalue problem (NIEP) consists of finding necessary and sufficient conditions for the existence of a nonnegative matrix with a given list of complex numbers as its spectrum
We deal with Leslie and doubly Leslie matrices
The analysis of a mathematical model that considers internal/external variables, and derives in spectral information that allow the behavior of the phenomenon shown in the model to be induced, is called the direct eigenvalues problem
Summary
Theorem 1. [17] Let (λ2 , . . . , λn ) be complex numbers with real parts less than or equal to zero and let ρ be a positive real number. H. Leslie (see References [13,18]), is an n × n nonnegative matrix of the form: a1. The doubly Leslie matrices were defined in Reference [20] as a generalization of a doubly companion matrix introduced in Reference [21]. N − 1, B is called doubly companion matrix which was introduced in Reference [21] by Butcher and Chartier. Λn be complex numbers with real parts less than or equal to zero, such that the list
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