当前位置: X-MOL 学术Linear Multilinear Algebra › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
On the positive semi-definite pth roots of positive semi-definite doubly stochastic matrices
Linear and Multilinear Algebra ( IF 0.9 ) Pub Date : 2020-09-16 , DOI: 10.1080/03081087.2020.1817296
Rafic Nader 1 , Bassam Mourad 2 , Hassan Abbas 2 , Alain Bretto 1
Affiliation  

In this note, we consider the problem of characterizing the conditions under which the positive semi-definite pth root of a positive semi-definite doubly stochastic matrix is doubly stochastic. First, we obtain new sufficient conditions for this problem that improve the existing ones for the case p = 2. In addition, if we let Kn denote the set of all n×n positive semi-definite doubly stochastic matrices, and if for any positive integer p, we define Kn1/p:={AKn:A1/p is doubly stochastic}, then our next result deals with proving that for n 3, the set Kn1/p is not convex but stars convex with respect to Jn which is the n×n matrix whose all entries are equal to 1/n. Next, we identify a large convex set that sits inside Kn1/p. Furthermore, we use the theory of M-matrices to present a method for constructing elements in Kn1/p. In the end, we investigate in depth the way of finding elements in Kn1/p via the use of eigenvalues.



中文翻译:

关于正半正定双随机矩阵的正半正定pth根

在本说明中,我们考虑表征正半正定双随机矩阵的正半正定p th 根是双随机的条件的问题。首先,我们为这个问题获得了新的充分条件,改进了p = 2情况下的现有充分条件 。此外,如果我们让ķn表示所有的集合n×n半正定双随机矩阵,如果对于任何正整数p,我们定义ķn1/p:={一个ķn一个1/p是双重随机的},那么我们的下一个结果就是证明n 3, 集合ķn1/p不是凸的,但星相对于凸Ĵn哪一个是n×n所有条目都等于 1/ n的矩阵。接下来,我们确定一个位于内部的大凸集ķn1/p. 此外,我们使用M矩阵的理论来提出一种构造元素的方法ķn1/p. 最后,我们深入研究了在ķn1/p通过使用特征值。

更新日期:2020-09-16
down
wechat
bug