Positivity properties of some special matrices

被引：4
|
作者：
Grover, Priyanka [1 ]
Panwar, Veer Singh [1 ]
Reddy, A. Satyanarayana [1 ]
机构：
[1] Shiv Nadar Univ, Dept Math, Dadri 201314, UP, India
来源：
LINEAR ALGEBRA AND ITS APPLICATIONS | 2020年 / 596卷
关键词：
Bell numbers; Infinitely divisible matrices; Positive semidefinite matrices; Schur product; Stirling numbers; Totally positive matrices; The beta function;
D O I：
10.1016/j.laa.2020.03.008
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
It is shown that for positive real numbers 0 < lambda(1) < ... < lambda(n), [1/beta(lambda i,lambda j)], where beta(.,.) denotes the beta function, is infinitely divisible and totally positive. For [1/beta(i,j)], the Cholesky decomposition and successive elementary bidiagonal decomposition are computed. Let to (n) be the nth Bell number. It is proved that [to(i + j)] is a totally positive matrix but is infinitely divisible only upto order 4. It is also shown that the symmetrized Stirling matrices are totally positive. (C) 2020 Elsevier Inc. All rights reserved.
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收藏
页码：203 / 215
页数：13
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