Weak log-majorization inequalities of singular values between normal matrices and their absolute values

Document Type: Research Paper

Authors

School of Mathematical Sciences‎, ‎Huaibei Normal University‎, ‎Huaibei 235000‎, P.R. ‎China.

Abstract

‎This paper presents two main results that the singular values of the Hadamard product of normal matrices $A_i$ are weakly log-majorized by the singular values of the Hadamard product of $|A_{i}|$ and the singular values of the sum of normal matrices $A_i$ are weakly log-majorized by the singular values of the sum of $|A_{i}|$‎. ‎Some applications to these inequalities are also given‎. ‎In addition‎, ‎several related and new inequalities are obtained‎.

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History

• Receive Date: 18 April 2014
• Revise Date: 23 November 2014
• Accept Date: 24 November 2014