A proof of Lee's conjecture on the sum of absolute values of matrices

被引：1

作者：

Lin, Jianfu ^{[1
]}

Zhang, Yun ^{[1
]}

机构：

[1] Huaibei Normal Univ, Sch Math Sci, Huaibei 235000, Peoples R China

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2022年 / 516卷 / 02期

基金：

美国国家科学基金会;

关键词：

Absolute value; Frobenius norm; Angles;

D O I：

10.1016/j.jmaa.2022.126542

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let broken vertical bar broken vertical bar center dot broken vertical bar broken vertical bar(F) denote the Frobenius norm of matrices and let |G| denote the absolute value of a square complex matrix G. We prove the following conjecture posed by Eun-Young Lee in 2010: broken vertical bar broken vertical bar A + B broken vertical bar broken vertical bar(F) <= root 1 + root 2/ 2 broken vertical bar broken vertical bar |A| + |B| broken vertical bar broken vertical bar(F) for any square complex matrices Aand Bof the same order, where the constant root 1+root 2/2 is best possible. (c) 2022 Elsevier Inc. All rights reserved.

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页数：6

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