The solvability conditions for the inverse eigenvalue problem of normal skew J-Hamiltonian matrices

Let [Formula: see text] be a normal matrix such that [Formula: see text] , where [Formula: see text] is an n-by-n identity matrix. In (S. Gigola, L. Lebtahi, N. Thome in Appl. Math. Lett. 48:36–40, 2015) it was introduced that a matrix [Formula: see text] is referred to as normal J-Hamiltonian if an...

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Detalles Bibliográficos
Autores principales: Zhao, Jia, Zhang, Jieming
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2018
Materias:
Research
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5884922/
https://www.ncbi.nlm.nih.gov/pubmed/29651221
http://dx.doi.org/10.1186/s13660-018-1667-1
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author Zhao, Jia
Zhang, Jieming
author_facet Zhao, Jia
Zhang, Jieming
author_sort Zhao, Jia
collection PubMed
description Let [Formula: see text] be a normal matrix such that [Formula: see text] , where [Formula: see text] is an n-by-n identity matrix. In (S. Gigola, L. Lebtahi, N. Thome in Appl. Math. Lett. 48:36–40, 2015) it was introduced that a matrix [Formula: see text] is referred to as normal J-Hamiltonian if and only if [Formula: see text] and [Formula: see text] . Furthermore, the necessary and sufficient conditions for the inverse eigenvalue problem of such matrices to be solvable were given. We present some alternative conditions to those given in the aforementioned paper for normal skew J-Hamiltonian matrices. By using Moore–Penrose generalized inverse and generalized singular value decomposition, the necessary and sufficient conditions of its solvability are obtained and a solvable general representation is presented.
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spelling pubmed-58849222018-04-10 The solvability conditions for the inverse eigenvalue problem of normal skew J-Hamiltonian matrices Zhao, Jia Zhang, Jieming J Inequal Appl Research Let [Formula: see text] be a normal matrix such that [Formula: see text] , where [Formula: see text] is an n-by-n identity matrix. In (S. Gigola, L. Lebtahi, N. Thome in Appl. Math. Lett. 48:36–40, 2015) it was introduced that a matrix [Formula: see text] is referred to as normal J-Hamiltonian if and only if [Formula: see text] and [Formula: see text] . Furthermore, the necessary and sufficient conditions for the inverse eigenvalue problem of such matrices to be solvable were given. We present some alternative conditions to those given in the aforementioned paper for normal skew J-Hamiltonian matrices. By using Moore–Penrose generalized inverse and generalized singular value decomposition, the necessary and sufficient conditions of its solvability are obtained and a solvable general representation is presented. Springer International Publishing 2018-04-04 2018 /pmc/articles/PMC5884922/ /pubmed/29651221 http://dx.doi.org/10.1186/s13660-018-1667-1 Text en © The Author(s) 2018 Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
spellingShingle Research
Zhao, Jia
Zhang, Jieming
The solvability conditions for the inverse eigenvalue problem of normal skew J-Hamiltonian matrices
title The solvability conditions for the inverse eigenvalue problem of normal skew J-Hamiltonian matrices
title_full The solvability conditions for the inverse eigenvalue problem of normal skew J-Hamiltonian matrices
title_fullStr The solvability conditions for the inverse eigenvalue problem of normal skew J-Hamiltonian matrices
title_full_unstemmed The solvability conditions for the inverse eigenvalue problem of normal skew J-Hamiltonian matrices
title_short The solvability conditions for the inverse eigenvalue problem of normal skew J-Hamiltonian matrices
title_sort solvability conditions for the inverse eigenvalue problem of normal skew j-hamiltonian matrices
topic Research
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5884922/
https://www.ncbi.nlm.nih.gov/pubmed/29651221
http://dx.doi.org/10.1186/s13660-018-1667-1
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