On the bisymmetric nonnegative inverse eigenvalue problem
| Autor: | Keng Wiboonton, Somchai Somphotphisut |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2015 |
| Předmět: |
Numerical Analysis
Pure mathematics Algebra and Number Theory 15A18 Diagonal 0211 other engineering and technologies Inverse 021107 urban & regional planning 010103 numerical & computational mathematics 02 engineering and technology 01 natural sciences Mathematics - Spectral Theory FOS: Mathematics Discrete Mathematics and Combinatorics Geometry and Topology Nonnegative matrix 0101 mathematics Complex number Spectral Theory (math.SP) Eigenvalues and eigenvectors Mathematics |
| Popis: | We study the bisymmetric nonnegative inverse eigenvalue problem (BNIEP). This problem is the problem of finding the necessary and sufficient conditions on a list of $n$ complex numbers to be a spectrum of an $n \times n$ bisymmetric nonnegative matrix. Most recently, some of the sufficient conditions for the BNIEP are given by Julio and Soto in 2015. In this article, we give another proof of one result (Theorem 4.3) in [Julio and Soto, 2015] and we obtain the result very similar to the one (Theorem 4.2) in [Julio and Soto, 2015] using a different method to construct our desired bisymmetric nonnegative matrix. We also give some sufficient conditions for the BNIEP based on the sufficient conditions for the nonnegative inverse eigenvalue problem (NIEP) given by Borobia in 1995. We give the condition that is both necessary and sufficient for the BNIEP when $n \leq 4$ and then we show that for $n = 6$, the BNIEP and the symmetric nonnegative eigenvalue problem (SNIEP) are different. Moreover, some sufficient conditions for the bisymmetric positive inverse eigenvalue problem are provided. Finally, we give a new result on a sufficient condition for the BNIEP with the prescribed diagonal entries. |
| Databáze: | OpenAIRE |
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