scholarly journals Corrigendum to “Maximal doubly stochastic matrix centralizers” [Linear Algebra Appl. 532 (2017) 387–396]

2018 ◽  
Vol 555 ◽  
pp. 432-433
Author(s):  
Henrique F. da Cruz ◽  
Gregor Dolinar ◽  
Rosário Fernandes ◽  
Bojan Kuzma
Keyword(s):  
Linear Algebra ◽  
Stochastic Matrix ◽  
Doubly Stochastic Matrix ◽  
Doubly Stochastic

Permanents of Random Doubly Stochastic Matrices

1974 ◽  
Vol 26 (3) ◽  
pp. 600-607 ◽  
Author(s):  
R. C. Griffiths
Keyword(s):  
Symmetric Group ◽  
Stochastic Matrix ◽  
Stochastic Matrices ◽  
Doubly Stochastic Matrix ◽  
Doubly Stochastic ◽  
Survey Article ◽  
Doubly Stochastic Matrices ◽  
Image Position

The permanent of an n × n matrix A = (aij) is defined aswhere Sn is the symmetric group of order n. For a survey article on permanents the reader is referred to [2]. An unresolved conjecture due to van der Waerden states that if A is an n × n doubly stochastic matrix; then per (A) ≧ n!/nn, with equality if and only if A = Jn = (1/n).

A Note Concerning Simultaneous Integral Equations

1968 ◽  
Vol 20 ◽  
pp. 855-861 ◽  
Author(s):  
Paul Knopp ◽  
Richard Sinkhorn
Keyword(s):  
Integral Equations ◽  
Stochastic Matrix ◽  
Diagonal Matrix ◽  
Main Diagonal ◽  
Doubly Stochastic Matrix ◽  
Doubly Stochastic ◽  
Scalar Multiple

In (2) Sinkhorn showed that corresponding to each positive n × n matrix A (i.e., every aij > 0) is a unique doubly stochastic matrix of the form D1AD2, where each Dk is a diagonal matrix with a positive main diagonal. The Dk themselves are unique up to a scalar multiple. In (3) the result was extended to show that D1AD2 could be made to have arbitrarypositive row and column sums (with the reservation, of course, that the sum of the row sums equal the sum of the column sums) where A need no longer be square.

The Term and Stochastic Ranks of a Matrix

1959 ◽  
Vol 11 ◽  
pp. 269-279 ◽  
Author(s):  
N. S. Mendelsohn ◽  
A. L. Dulmage
Keyword(s):  
Real Number ◽  
Stochastic Matrix ◽  
Real Numbers ◽  
Doubly Stochastic Matrix ◽  
Doubly Stochastic ◽  
The Matrix ◽  
Term Rank ◽  
Square Matrix

The term rank p of a matrix is the order of the largest minor which has a non-zero term in the expansion of its determinant. In a recent paper (1), the authors made the following conjecture. If S is the sum of all the entries in a square matrix of non-negative real numbers and if M is the maximum row or column sum, then the term rank p of the matrix is greater than or equal to the least integer which is greater than or equal to S/M. A generalization of this conjecture is proved in § 2.The term doubly stochastic has been used to describe a matrix of nonnegative entries in which the row and column sums are all equal to one. In this paper, by a doubly stochastic matrix, the, authors mean a matrix of non-negative entries in which the row and column sums are all equal to the same real number T.

Linear preservers of Hadamard majorization

2016 ◽  
Vol 31 ◽  
pp. 593-609 ◽  
Author(s):  
Sara Motlaghian ◽  
Ali Armandnejad ◽  
Frank Hall
Keyword(s):  
Stochastic Matrix ◽  
Doubly Stochastic Matrix ◽  
Graph Theoretic ◽  
Doubly Stochastic ◽  
Linear Preservers ◽  
Linear Maps ◽  
Term Rank

Let $\textbf{M}_{n }$ be the set of all $n \times n $ realmatrices. A matrix $D=[d_{ij}]\in\textbf{M}_{n } $ with nonnegative entries is called doubly stochastic if $\sum_{k=1}^{n} d_{ik}=\sum_{k=1}^{n} d_{kj}=1$ for all $1\leq i,j\leq n$. For $ X,Y \in \textbf{M}_{n}$ we say that $X$ is Hadamard-majorized by $Y$, denoted by $ X\prec_{H} Y$, if there exists an $n \times n$ doubly stochastic matrix $D$ such that $X=D\circ Y$.In this paper, some properties of$\prec_{H}$ on $\textbf{M}_{n}$ are first obtained, and then the (strong) linear preservers of$\prec_{H}$ on $\textbf{M}_{n }$ are characterized. For $n\geq3$, it is shown that the strong linear preservers of Hadamard majorization on $\textbf{M}_{n}$ are precisely the invertible linear maps on $\textbf{M}_{n}$ which preserve the set of matrices of term rank 1.An interesting graph theoretic connection to the linear preservers of Hadamard majorization is exhibited. A number of examples are also provided in the paper.

scholarly journals G-tridiagonal majorization on M n,m

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Ahmad Mohammadhasani ◽  
Yamin Sayyari ◽  
Mahdi Sabzvari
Keyword(s):  
Stochastic Matrix ◽  
Doubly Stochastic Matrix ◽  
Doubly Stochastic ◽  
Linear Preservers

Abstract For X, Y ∈ M n,m , it is said that X is g-tridiagonal majorized by Y (and it is denoted by X ≺ gt Y) if there exists a tridiagonal g-doubly stochastic matrix A such that X = AY. In this paper, the linear preservers and strong linear preservers of ≺ gt are characterized on M n,m .

scholarly journals Maximal doubly stochastic matrix centralizers

2017 ◽  
Vol 532 ◽  
pp. 387-396 ◽  
Author(s):  
Henrique F. da Cruz ◽  
Gregor Dolinar ◽  
Rosário Fernandes ◽  
Bojan Kuzma
Keyword(s):  
Stochastic Matrix ◽  
Doubly Stochastic Matrix ◽  
Doubly Stochastic
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