The inverse eigenvalue problem for nonnegative matrices

Šmigoc, Helena

doi:10.1016/j.laa.2004.03.036

Cited by 54 publications

(44 citation statements)

References 6 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Note that Nazari and Sherafat's result can also be obtained from an earlier perturbation result in [23,Theorem 11] and is quoted below. Also, the result of Theorem 3.1 can be directly extended to the symmetric nonnegative matrices and has been discussed in [24,Theorem 8].…”

Section: Conquering Proceduressupporting

confidence: 58%

An algorithm for constructing nonnegative matrices with prescribed real eigenvalues

Lin

2015

Applied Mathematics and Computation

View full text Add to dashboard Cite

Section: Conquering Proceduressupporting

confidence: 58%

An algorithm for constructing nonnegative matrices with prescribed real eigenvalues

Lin

2015

Applied Mathematics and Computation

View full text Add to dashboard Cite

“…, p 0 , we Downloaded by [New York University] at 08:40 04 August 2015 may compute the solution A + XC X T in just one step. We also point out that the result in [17,Lemma 5] follows from Rado's Theorem 1.1: Suppose we have an n × n matrix A with spectrum {λ 1 , . .…”

Section: New Sufficient Conditions For the Nniepmentioning

confidence: 97%

“…. , λ n are eigenvalues of + C X = A. In[16, Theorem 8], a result whose origin is the Ref [17],. the authors show how to construct new symmetrically realizable lists from known symmetrically realizable lists.…”

mentioning

confidence: 99%

Normal nonnegative realization of spectra

Julio

Manzaneda

Soto

2014

Linear and Multilinear Algebra

View full text Add to dashboard Cite

The nonnegative inverse eigenvalue problem is the problem of finding necessary and sufficient conditions for the existence of an n × n entrywise nonnegative matrix A with prescribed spectrum. This problem remains open for n ≥ 5. If the matrix A is required to be normal, the problem will be called the normal nonnegative inverse eigenvalue problem (NNIEP). Sufficient conditions for a list of complex numbers to be the spectrum of a normal nonnegative matrix were obtained by Xu [Linear Multilinear Algebra. 1993;34:353-364]. In this paper, we give a normal version of a rank-r perturbation result due to Rado and published by Perfect [Duke Math. J. 1955;22:305-311], which allow us to obtain new sufficient conditions for the NNIEP to have a solution. These new conditions significantly improve Xu's conditions. We also apply our results to construct nonnegative matrices with arbitrarily prescribed elementary divisors.

show abstract

“…It has been studied in its general form in e.g. [2,6,8,9,12,22,23,26]. When the realizing nonnegative matrix is required to be symmetric (with, of course, real eigenvalues) the problem is designated by symmetric nonnegative inverse eigenvalue problem (SNIEP) and it is also an open problem.…”

Section: Introductionmentioning

confidence: 99%

Realizable lists via the spectra of structured matrices

Manzaneda

Andrade

Robbiano

2017

Linear Algebra and its Applications

View full text Add to dashboard Cite

A square matrix of order n with n ≥ 2 is called a permutative matrix or permutative when all its rows (up to the first one) are permutations of precisely its first row. In this paper, the spectra of a class of permutative matrices are studied. In particular, spectral results for matrices partitioned into 2-by-2 symmetric blocks are presented and, using these results sufficient conditions on a given list to be the list of eigenvalues of a nonnegative permutative matrix are obtained and the corresponding permutative matrices are constructed. Guo perturbations on given lists are exhibited.

show abstract

The inverse eigenvalue problem for nonnegative matrices

Cited by 54 publications

References 6 publications

An algorithm for constructing nonnegative matrices with prescribed real eigenvalues

An algorithm for constructing nonnegative matrices with prescribed real eigenvalues

Normal nonnegative realization of spectra

Realizable lists via the spectra of structured matrices

Contact Info

Product

Resources

About