On Spectral Properties of Doubly Stochastic Matrices

On Spectral Properties of Doubly Stochastic Matrices

The relationship among eigenvalues, singular values, and quadratic forms associated with linear transforms of doubly stochastic matrices has remained an important topic since 1949. The main objective of this article is to present some useful theorems, concerning the spectral properties of doubly sto...

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Main Authors: Mutti-Ur Rehman, Jehad Alzabut, Javed Hussain Brohi, Arfan Hyder
Format: Article
Language:English
Published: MDPI AG 2020-03-01
Series:Symmetry
Subjects:
doubly stochastic matrices
eigenvalues
singular values
sturctured singular values
odes
Online Access:https://www.mdpi.com/2073-8994/12/3/369
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spelling doaj-ee67d73966dc4d309b26ed9f2ef038902020-11-24T21:53:48ZengMDPI AGSymmetry2073-89942020-03-0112336910.3390/sym12030369sym12030369On Spectral Properties of Doubly Stochastic MatricesMutti-Ur Rehman0Jehad Alzabut1Javed Hussain Brohi2Arfan Hyder3Department of Mathematics, Sukkur IBA University, Sukkur 65200, PakistanDepartment of Mathematics and General Sciences, Prince Sultan University, Riyadh 11586, Saudi ArabiaDepartment of Mathematics, Sukkur IBA University, Sukkur 65200, PakistanDepartment of Mathematics, Sukkur IBA University, Sukkur 65200, PakistanThe relationship among eigenvalues, singular values, and quadratic forms associated with linear transforms of doubly stochastic matrices has remained an important topic since 1949. The main objective of this article is to present some useful theorems, concerning the spectral properties of doubly stochastic matrices. The computation of the bounds of structured singular values for a family of doubly stochastic matrices is presented by using low-rank ordinary differential equations-based techniques. The numerical computations illustrating the behavior of the method and the spectrum of doubly stochastic matrices is then numerically analyzed.https://www.mdpi.com/2073-8994/12/3/369doubly stochastic matriceseigenvaluessingular valuessturctured singular valuesodes
collection DOAJ
language English
format Article
sources DOAJ
author Mutti-Ur Rehman
Jehad Alzabut
Javed Hussain Brohi
Arfan Hyder
spellingShingle Mutti-Ur Rehman
Jehad Alzabut
Javed Hussain Brohi
Arfan Hyder
On Spectral Properties of Doubly Stochastic Matrices
Symmetry
doubly stochastic matrices
eigenvalues
singular values
sturctured singular values
odes
author_facet Mutti-Ur Rehman
Jehad Alzabut
Javed Hussain Brohi
Arfan Hyder
author_sort Mutti-Ur Rehman
title On Spectral Properties of Doubly Stochastic Matrices
title_short On Spectral Properties of Doubly Stochastic Matrices
title_full On Spectral Properties of Doubly Stochastic Matrices
title_fullStr On Spectral Properties of Doubly Stochastic Matrices
title_full_unstemmed On Spectral Properties of Doubly Stochastic Matrices
title_sort on spectral properties of doubly stochastic matrices
publisher MDPI AG
series Symmetry
issn 2073-8994
publishDate 2020-03-01
description The relationship among eigenvalues, singular values, and quadratic forms associated with linear transforms of doubly stochastic matrices has remained an important topic since 1949. The main objective of this article is to present some useful theorems, concerning the spectral properties of doubly stochastic matrices. The computation of the bounds of structured singular values for a family of doubly stochastic matrices is presented by using low-rank ordinary differential equations-based techniques. The numerical computations illustrating the behavior of the method and the spectrum of doubly stochastic matrices is then numerically analyzed.
topic doubly stochastic matrices
eigenvalues
singular values
sturctured singular values
odes
url https://www.mdpi.com/2073-8994/12/3/369
work_keys_str_mv AT muttiurrehman onspectralpropertiesofdoublystochasticmatrices
AT jehadalzabut onspectralpropertiesofdoublystochasticmatrices
AT javedhussainbrohi onspectralpropertiesofdoublystochasticmatrices
AT arfanhyder onspectralpropertiesofdoublystochasticmatrices
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