Characterization,parity, and power sequences of locally finite doubly stochastic matrices

We show that infinite locally finite doubly stochastic matrices are particular limits of sequences of finite doubly stochastic matrices and reciprocally. Thereby, we define the parity in the set of infinite locally finite doubly stochastic matrices. In particular, convexity and stability properties of the even matrix of this set are investigated, as well as the differences between the finite case and the infinite case. Moreover, the limits of the powers of locally finite infinite doubly stochastic matrices in this context are determined.     

On a Lie-theoretic approach to generalized doubly stochastic matrices and applications

In this article, we study generalized doubly stochastic matrices using the theory of Lie groups and Lie algebras. Applications to the inverse eigenvalue problem for symmetric doubly stochastic matrices are presented.     

On a Lie-theoretic approach to generalized doubly stochastic matrices and applications

In this article, we study generalized doubly stochastic matrices using the theory of Lie groups and Lie algebras. Applications to the inverse eigenvalue problem for symmetric doubly stochastic matrices are presented.     

Vertex degrees and doubly stochastic graph matrices

In this article, the relationship between vertex degrees and entries of the doubly stochastic graph matrix has been investigated. In particular, we present an upper bound for the main diagonal entries of a doubly stochastic graph matrix and investigate the relations between a kind of distance for graph vertices and the vertex degrees. These results are used to answer in negative Merris' question on doubly stochastic graph matrices. These results may also be used to establish relations between graph structure and entries of doubly stochastic graph matrices. © 2010 Wiley Periodicals, Inc. J Graph Theory 66:104‐114, 2011     

具有位数3和4的双随机循环矩阵中的素元

本文研究了双随机循环矩阵中素元的分类问题．由于任一n阶双随机循环矩阵都可以唯一地表示为移位的n-1次一元多项式,从而可把双随机循环矩阵中素元的分类问题简化为解双随机循环矩阵上的一个方程．应用此原理,本文完全解决了判别具有位数3的n阶双随机循环矩阵是否为素元的问题,并给出了n阶双随机循环矩阵中一类具有位数4的素元．     

对称双随机矩阵逆特征值问题

主要研究随机矩阵逆特征值问题．特别是对称双随机矩阵和列随机矩阵逆特征值问题．对参考文献[1]与[2]的结论作了一些推广．并给出了—个数值例子．     

Doubly stochastic matrices of trees

In this paper, we obtain sharp upper and lower bounds for the smallest entries of doubly stochastic matrices of trees and characterize all extreme graphs which attain the bounds. We also present a counterexample to Merris’ conjecture on relations between the smallest entry of the doubly stochastic matrix and the algebraic connectivity of a graph in [R. Merris, Doubly stochastic graph matrices II, Linear Multilinear Algebr. 45 (1998) 275–285].     

Full ordering in the Shorrocks mobility sense of the semiring of monotone doubly stochastic matrices

In this paper, we investigate the ordering on a semiring of monotone doubly stochastic transition matrices in Shorrocks’ sense. We identify a class of an equilibrium index of mobility that induces the full ordering in a semiring, while this ordering is compatible with Dardanoni’s partial ordering on a set of monotone primitive irreducible doubly stochastic matrices.     

Topological properties of orthostochastic matrices

The set of n×n orthostochastic matrices with the topology induced by the Euclidean matric is shown to be compact and path-connected. For n<3, the set of orthostochastic matrices is identical to the set of doubly stochastic matrices. In this paper, it is shown that for n3 the orthostochastic matrices are not everywhere dense in the set of doubly stochastic matrices, thus answering a question of L. Mirsky in his survey article on doubly stochastic matrices [2].     

Permanents of special classes of doubly stochastic matrices

We identify the doubly stochastic matrices with at least one zero entry which are closest in the Euclidean norm to J_n, the matrix with each entry equal to 1/n, and we show that at these matrices the permanent function has a relative minimum when restricted to doubly stochastic matrices having zero entries.     

广义双随机矩阵反问题及其应用

研究广义双随机矩阵反问题.给出广义双随机矩阵的最小二乘解,得到了解的具体表达形式.并讨论了用广义双随机矩阵构造给定矩阵的最佳逼近问题,给出该问题有解的充分必要条件和解的表达形式.包括算法及数值例子.     

Generalization of some results concerning eigenvalues of a certain class of matrices and some applications

In this note, we present a generalization of some results concerning the spectral properties of a certain class of block matrices. As applications, we study some of its implications on nonnegative matrices and doubly stochastic matrices as well as on graph spectra and graph energy.     

Minimum Permanents of Tridiagonal Doubly Stochastic Matrices

We determine the minimum permanents and minimizing matrices of the tridiagonal doubly stochastic matrices and of certain doubly stochastic matrices with prescribed zero entries.     

On the Hamiltonicity Gap and doubly stochastic matrices

We consider the Hamiltonian cycle problem embedded in singularly perturbed (controlled) Markov chains. We also consider a functional on the space of stationary policies of the process that consists of the (1,1)‐entry of the fundamental matrices of the Markov chains induced by these policies. We focus on the subset of these policies that induce doubly stochastic probability transition matrices which we refer to as the “doubly stochastic policies.” We show that when the perturbation parameter, ε, is sufficiently small, the minimum of this functional over the space of the doubly stochastic policies is attained at a Hamiltonian cycle, provided that the graph is Hamiltonian. We also show that when the graph is non‐Hamiltonian, the above minimum is strictly greater than that in a Hamiltonian case. We call the size of this difference the “Hamiltonicity Gap” and derive a conservative lower bound for this gap. Our results imply that the Hamiltonian cycle problem is equivalent to the problem of minimizing the variance of the first hitting time of the home node, over doubly stochastic policies. © 2008 Wiley Periodicals, Inc. Random Struct. Alg., 2009     

Minimum Permanents of Tridiagonal Doubly Stochastic Matrices

We determine the minimum permanents and minimizing matrices of the tridiagonal doubly stochastic matrices and of certain doubly stochastic matrices with prescribed zero entries.     

Matrices which commute with doubly stochastic matrices

The set doubly stochastic matrices which commute with the doubly stochastic matrices of any particular given rank is determined.     

Matrices which commute with doubly stochastic matrices

The set doubly stochastic matrices which commute with the doubly stochastic matrices of any particular given rank is determined.     

Directed graphs,Hamiltonicity and doubly stochastic matrices

We consider the Hamiltonian cycle problem embedded in singularly perturbed (controlled) Markov chains. We also consider a functional on the space of stationary policies of the process that consists of the (1,1)‐entry of the fundamental matrices of the Markov chains induced by the same policies. In particular, we focus on the subset of these policies that induce doubly stochastic probability transition matrices, which we refer to as the “doubly stochastic policies.” We show that when the perturbation parameter ? is sufficiently small the minimum of this functional over the space of the doubly stochastic policies is attained very close to a Hamiltonian cycle, provided that the graph is Hamiltonian. We also derive precise analytical expressions for the elements of the fundamental matrix that lend themselves to probabilistic interpretation as well as asymptotic expressions for the first diagonal element, for a variety of deterministic policies that are of special interest, including those that correspond to Hamiltonian cycles. © 2004 Wiley Periodicals, Inc. Random Struct. Alg., 2004     

Row Stochastic Matrices Similar to Doubly Stochastic Matrices

The problem of determining which row stochastic n-by-n matrices are similar to doubly stochastic matrices is considered. That not all are is indicated by example, and an abstract characterization as well as various explicit sufficient conditions are given. For example, if a row stochastic matrix has no entry smaller than (n+1)^-1 it is similar to a doubly stochastic matrix.

Relaxing the nonnegativity requirement, the real matrices which are similar to real matrices with row and column sums one are then characterized, and it is observed that all row stochastic matrices have this property. Some remarks are then made on the nonnegative eigenvalue problem with respect to i) a necessary trace inequality and ii) removing zeroes from the spectrum.     

A minimal completion of (0, 1)-matrices without total support

In this paper, we provide a method to complete a (0, 1)-matrix without total support via the minimal doubly stochastic completion of doubly substochastic matrices and show that the size of the completion is determined by the maximum diagonal sum or the term rank of the given (0, 1)-matrix.