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Article

On Spectral Properties of Doubly Stochastic Matrices

1
Department of Mathematics, Sukkur IBA University, Sukkur 65200, Pakistan
2
Department of Mathematics and General Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia
*
Author to whom correspondence should be addressed.
Symmetry 2020, 12(3), 369; https://doi.org/10.3390/sym12030369
Received: 7 February 2020 / Revised: 22 February 2020 / Accepted: 27 February 2020 / Published: 2 March 2020
(This article belongs to the Special Issue Symmetry in Numerical Linear and Multilinear Algebra)
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. View Full-Text
Keywords: doubly stochastic matrices; eigenvalues; singular values; sturctured singular values; ODEs doubly stochastic matrices; eigenvalues; singular values; sturctured singular values; ODEs
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MDPI and ACS Style

Rehman, M.-U.; Alzabut, J.; Brohi, J.H.; Hyder, A. On Spectral Properties of Doubly Stochastic Matrices. Symmetry 2020, 12, 369. https://doi.org/10.3390/sym12030369

AMA Style

Rehman M-U, Alzabut J, Brohi JH, Hyder A. On Spectral Properties of Doubly Stochastic Matrices. Symmetry. 2020; 12(3):369. https://doi.org/10.3390/sym12030369

Chicago/Turabian Style

Rehman, Mutti-Ur, Jehad Alzabut, Javed H. Brohi, and Arfan Hyder. 2020. "On Spectral Properties of Doubly Stochastic Matrices" Symmetry 12, no. 3: 369. https://doi.org/10.3390/sym12030369

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