Frontiers of Mathematics in China >

2016 , Vol. 11 >Issue 3: 647 - 659

DOI: https://doi.org/10.1007/s11464-016-0533-z

RESEARCH ARTICLE

Counting extreme U1 matrices and characterizing quadratic doubly stochastic operators

  • Quanbing ZHANG ,
  • Shangjun YANG
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  • Key Laboratory of Intelligent Computing & Signal Processing, Ministry of Education, Anhui University, Hefei 230039, China

Received date: 04 Mar 2015

Accepted date: 29 Feb 2016

Published date: 17 May 2016

Copyright

2014 Higher Education Press and Springer-Verlag Berlin Heidelberg
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Abstract

The U1 matrix and extreme U1 matrix were successfully used to study quadratic doubly stochastic operators by R. Ganikhodzhaev and F. Shahidi [Linear Algebra Appl., 2010, 432: 24–35], where a necessary condition for a U1 matrix to be extreme was given. S. Yang and C. Xu [Linear Algebra Appl., 2013, 438: 3905–3912] gave a necessary and sufficient condition for a symmetric nonnegative matrix to be an extreme U1 matrix and investigated the structure of extreme U1 matrices. In this paper, we count the number of the permutation equivalence classes of the n × n extreme U1 matrices and characterize the structure of the quadratic stochastic operators and the quadratic doubly stochastic operators.

Key words： Extreme U1 matrix; quadratic doubly stochastic operator; majorized; permutation similar; irreducible matrix

Cite this article

Quanbing ZHANG , Shangjun YANG . Counting extreme U1 matrices and characterizing quadratic doubly stochastic operators[J]. Frontiers of Mathematics in China, 2016 , 11(3) : 647 -659 . DOI: 10.1007/s11464-016-0533-z

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Yang S, Xu C. On extreme U1matrices. Linear Algebra Appl, 2013, 438: 3905–3912

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