加权海灵格距离和中间性

IF 0.9 4区数学 Q2 MATHEMATICS

Mathematical Inequalities & Applications Pub Date : 2021-01-01 DOI:10.7153/MIA-2021-24-11

T. Dinh, C. Lê, B. K. Vo, T. Vuong

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引用次数: 1

摘要

本文引入了矩阵的加权海灵格距离，它是欧几里得距离和海灵格距离之间的插值。我们证明了加权海灵格距离和Alpha Procrustes距离的等价性。由此证明了矩阵幂均值μp(t, a,B) = (tAp +(1−t)Bp)1/p在加权Hellinger和Alpha Procrustes距离上满足中间性。数学学科分类(2010):47A63, 47A56。

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Weighted Hellinger distance and in-betweenness property

In this paper we introduce the weighted Hellinger distance for matrices which is an interpolating between the Euclidean distance and the Hellinger distance. We show the equivalence of the weighted Hellinger distance and the Alpha Procrustes distance. As a consequence, we prove that the matrix power mean μp(t,A,B) = (tAp +(1−t)Bp)1/p satisfies in-betweenness property in the weighted Hellinger and Alpha Procrustes distances. Mathematics subject classification (2010): 47A63, 47A56.

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来源期刊

Mathematical Inequalities & Applications 数学-数学

CiteScore

2.30

自引率

10.00%

发文量

审稿时长

6-12 weeks

期刊介绍： ''Mathematical Inequalities & Applications'' (''MIA'') brings together original research papers in all areas of mathematics, provided they are concerned with inequalities or their role. From time to time ''MIA'' will publish invited survey articles. Short notes with interesting results or open problems will also be accepted. ''MIA'' is published quarterly, in January, April, July, and October.