Counting extreme \(U_1\) matrices and characterizing quadratic doubly stochastic operators
type: Item
instance of: scholarly article
title: Counting extreme \(U_1\) matrices and characterizing quadratic doubly stochastic operators
zbMATH Open document ID: 1367.15054
author: Quanbing Zhang
author: Shangjun Yang
published in: Frontiers of Mathematics in China
publication date: 2017-05-12T00:00:00Z
review text: The \(U_1\) matrix and extreme \(U_1\) matrix were successfully used to study quadratic doubly stochastic operators by \textit{R. Ganikhodzhaev} and \textit{F. Shahidi} [Linear Algebra Appl. 432, No. 1, 24--35 (2010; Zbl 1186.15025)], where a necessary condition for a \(U_1\) matrix to be extreme was given. \textit{S. Yang} and \textit{C. Xu} [Linear Algebra Appl. 438, No. 10, 3905--3912 (2013; Zbl 1305.15025)] gave a necessary and sufficient condition for a symmetric nonnegative matrix to be an extreme \(U_1\) matrix and investigated the structure of extreme \(U_1\) matrices. In this paper, the authors count the number of the permutation equivalence classes of the \(n\times n\) extreme \(U_1\) matrices and characterize the structure of the quadratic stochastic operators and the quadratic doubly stochastic operators.
reviewed by: Huang Wenxue
Mathematics Subject Classification ID: 15B51
Mathematics Subject Classification ID: 15A18
zbMATH DE Number: 6714854
zbMATH Keywords: doubly stochastic operator
zbMATH Keywords: extreme
zbMATH Keywords: irreducible matrix
zbMATH Keywords: permutation similar
zbMATH Keywords: quadratic majorized
zbMATH Keywords: \(U_1\) matrix
MaRDI profile type: Publication
full work available at URL: s11464-016-0533-z
OpenAlex ID: W2334720489
cites work: Q3943082
cites work: Q5834711
cites work: Doubly stochastic quadratic operators and Birkhoff's problem
cites work: Matrix Analysis
cites work: The number of trees
cites work: On Dissipative Quadratic Stochastic Operators
cites work: On extreme \(U_1\) matrices
DOI: 10.1007/S11464-016-0533-Z
description: scientific article; zbMATH DE number 6714854