scholarly journals On Spectral Properties of Doubly Stochastic Matrices

Symmetry ◽  
2020 ◽  
Vol 12 (3) ◽  
pp. 369
Author(s):  
Mutti-Ur Rehman ◽  
Jehad Alzabut ◽  
Javed Hussain Brohi ◽  
Arfan Hyder
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Quadratic Forms ◽  
Spectral Properties ◽  
Singular Values ◽  
Low Rank ◽  
Stochastic Matrices ◽  
Doubly Stochastic ◽  
Doubly Stochastic Matrices ◽  
The Relationship

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.

STRUCTURED SINGULAR VALUES OF SOME GENERALISED STOCHASTIC MATRICES

2021 ◽  
pp. 1-10
Author(s):  
KIJTI RODTES ◽  
MUTTI UR REHMAN ABBASI
Keyword(s):  
Special Class ◽  
Singular Values ◽  
Circulant Matrices ◽  
Stochastic Matrices ◽  
Complex Matrices ◽  
Doubly Stochastic ◽  
Doubly Stochastic Matrices

Abstract We investigate a class of generalised stochastic complex matrices constructed from the class of all doubly stochastic matrices and a special class of circulant matrices. We determine the exact values of the structured singular values of all matrices in the class in terms of the constant row (column) sum.

scholarly journals A Note on Eigenvalues Location for Trace Zero Doubly Stochastic Matrices

2015 ◽  
Vol 30 ◽  
pp. 599-604 ◽  
Author(s):  
Luca Benvenuti
Keyword(s):  
Spectral Properties ◽  
Stochastic Matrices ◽  
Doubly Stochastic ◽  
Doubly Stochastic Matrices

Some results on the location of the eigenvalues of trace zero doubly stochastic matrices are provided. A result similar to that provided in [H. Perfect and L. Mirsky. Spectral properties of doubly–stochastic matrices. Monatshefte fur Mathematik, 69(1):35–57, 1965.] for doubly stochastic matrices is given.

A nonlocal problem for a differential operator of even order with involution

2020 ◽  
Vol 26 (2) ◽  
pp. 297-307
Author(s):  
Petro I. Kalenyuk ◽  
Yaroslav O. Baranetskij ◽  
Lubov I. Kolyasa
Keyword(s):  
Differential Operator ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Riesz Basis ◽  
Existence And Uniqueness ◽  
Spectral Properties ◽  
Nonlocal Problem ◽  
Even Order

AbstractWe study a nonlocal problem for ordinary differential equations of {2n}-order with involution. Spectral properties of the operator of this problem are analyzed and conditions for the existence and uniqueness of its solution are established. It is also proved that the system of eigenfunctions of the analyzed problem forms a Riesz basis.

The Geometry of d2y1/dt2 = f (y, ẏ, t) and d2y2/dt2 = g(y, ẏ, t), and Euclidean Spaces

2006 ◽  
Vol 49 (2) ◽  
pp. 170-184
Author(s):  
Richard Atkins
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Shortest Paths ◽  
Equivalence Problem ◽  
Second Order ◽  
System Of Differential Equations ◽  
Lagrange Equations ◽  
Invariant Functions ◽  
Underlying Geometry ◽  
The Relationship

AbstractThis paper investigates the relationship between a system of differential equations and the underlying geometry associated with it. The geometry of a surface determines shortest paths, or geodesics connecting nearby points, which are defined as the solutions to a pair of second-order differential equations: the Euler–Lagrange equations of the metric. We ask when the converse holds, that is, when solutions to a system of differential equations reveals an underlying geometry. Specifically, when may the solutions to a given pair of second order ordinary differential equations d2y1/dt2 = f (y, ẏ, t) and d2y2/dt2 = g(y, ẏ, t) be reparameterized by t → T(y, t) so as to give locally the geodesics of a Euclidean space? Our approach is based upon Cartan's method of equivalence. In the second part of the paper, the equivalence problem is solved for a generic pair of second order ordinary differential equations of the above form revealing the existence of 24 invariant functions.

scholarly journals Positional Voting and Doubly Stochastic Matrices

2021 ◽  
Vol 128 (4) ◽  
pp. 337-351
Author(s):  
Jacqueline Anderson ◽  
Brian Camara ◽  
John Pike
Keyword(s):  
Stochastic Matrices ◽  
Doubly Stochastic ◽  
Doubly Stochastic Matrices ◽  
Positional Voting
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