A map of sufficient conditions for the real nonnegative inverse eigenvalue problem
نویسندگان
چکیده
منابع مشابه
On the nonnegative inverse eigenvalue problem of traditional matrices
In this paper, at first for a given set of real or complex numbers $sigma$ with nonnegative summation, we introduce some special conditions that with them there is no nonnegative tridiagonal matrix in which $sigma$ is its spectrum. In continue we present some conditions for existence such nonnegative tridiagonal matrices.
متن کاملOn the Comparison of Sufficient Conditions for the Real and Symmetric Nonnegative Inverse Eigenvalue Problems
The real nonnegative inverse eigenvalue problem (RNIEP) is the problem of characterizing all possible real spectra of entrywise nonnegative matrices. This problem remains unsolved. Since the first result in this area announced by Suleimanova in 1949 and proved by Perfect in 1953, a number of realizability criteria or sufficient conditions for the existence of a nonnegative matrix with a given r...
متن کاملNonnegative Inverse Eigenvalue Problem
Nonnegative matrices have long been a sorce of interesting and challenging mathematical problems. They are real matrices with all their entries being nonnegative and arise in a num‐ ber of important application areas: communications systems, biological systems, economics, ecology, computer sciences, machine learning, and many other engineering systems. Inverse eigenvalue problems constitute an ...
متن کاملon the nonnegative inverse eigenvalue problem of traditional matrices
in this paper, at rst for a given set of real or complex numbers with nonnegative summation, we introduce some special conditions that with them there is no nonnegative tridiagonal matrix in which is its spectrum. in continue we present some conditions for existence such nonnegative tridiagonal matrices.
متن کاملThe real nonnegative inverse eigenvalue problem is NP-hard
A list of complex numbers is realizable if it is the spectrum of a nonnegative matrix. In 1949 Sulěımanova posed the nonnegative inverse eigenvalue problem (NIEP): the problem of determining which lists of complex numbers are realizable. The version for reals of the NIEP (RNIEP) asks for realizable lists of real numbers. In the literature there are many sufficient conditions or criteria for lis...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2007
ISSN: 0024-3795
DOI: 10.1016/j.laa.2007.05.046