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Counting extreme U1 matrices and characterizing quadratic doubly stochastic operators |
Quanbing ZHANG( ),Shangjun YANG |
| Key Laboratory of Intelligent Computing & Signal Processing, Ministry of Education, Anhui University, Hefei 230039, China |
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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.
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| Keywords
Extreme U1 matrix
quadratic doubly stochastic operator
majorized
permutation similar
irreducible matrix
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Corresponding Author(s):
Quanbing ZHANG
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Issue Date: 17 May 2016
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Yang S, Xu C. On extreme U1matrices. Linear Algebra Appl, 2013, 438: 3905–3912
https://doi.org/10.1016/j.laa.2011.12.022
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