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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