随机向量诱导的复矩阵范数

IF 0.5 4区数学 Q3 MATHEMATICS Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques Pub Date : 2022-11-15 DOI:10.4153/S0008439522000741

Ángel Chávez, S. Garcia, Jackson Hurley

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引用次数: 2

摘要

摘要我们在$n\timesn$复矩阵上引入了一个范数族。这些规范产生于概率框架，它们的构建和验证涉及概率论、划分组合学和非交换变量中的跟踪多项式。因此，我们得到了完全齐次对称多项式的Hunter正性定理的推广。

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Norms on complex matrices induced by random vectors

Abstract We introduce a family of norms on the $n \times n$ complex matrices. These norms arise from a probabilistic framework, and their construction and validation involve probability theory, partition combinatorics, and trace polynomials in noncommuting variables. As a consequence, we obtain a generalization of Hunter’s positivity theorem for the complete homogeneous symmetric polynomials.

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来源期刊

Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques 数学-数学

CiteScore

1.30

自引率

0.00%

发文量

审稿时长

24 months

期刊介绍： The Canadian Mathematical Bulletin was established in 1958 to publish original, high-quality research papers in all branches of mathematics and to accommodate the growing demand for shorter research papers. The Bulletin is a companion publication to the Canadian Journal of Mathematics that publishes longer papers. New research papers are published continuously online and collated into print issues four times each year. To be submitted to the Bulletin, papers should be at most 18 pages long and may be written in English or in French. Longer papers should be submitted to the Canadian Journal of Mathematics. Fondé en 1958, le Bulletin canadien de mathématiques (BCM) publie des articles d’avant-garde et de grande qualité dans toutes les branches des mathématiques, de même que pour répondre à la demande croissante d’articles scientifiques plus brefs. Le BCM se veut une publication complémentaire au Journal canadien de mathématiques, qui publie de longs articles. En ligne, il propose constamment de nouveaux articles de recherche, puis les réunit dans des numéros imprimés quatre fois par année. Les textes présentés au BCM doivent compter au plus 18 pages et être rédigés en anglais ou en français. C’est le Journal canadien de mathématiques qui reçoit les articles plus longs.

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EISENSTEIN CONGRUENCES AMONG EULER SYSTEMS Norms on complex matrices induced by random vectors II: extension of weakly unitarily invariant norms Bregman Distance Regularization for Nonsmooth and Nonconvex Optimization SOME RESULTS ON VARIOUS TYPES OF COMPACTNESS OF WEAK* DUNFORD-PETTIS OPERATORS ON BANACH LATTICES BCM volume 66 issue 4 Cover and Front matter