%0 Journal Article %T Weak log-majorization inequalities of singular values between normal matrices and their absolute values %J Bulletin of the Iranian Mathematical Society %I Iranian Mathematical Society (IMS) %Z 1017-060X %A Chen, D. %A Zhang, Y. %D 2016 %\ 02/01/2016 %V 42 %N 1 %P 143-153 %! Weak log-majorization inequalities of singular values between normal matrices and their absolute values %K Unitarily invariant norms‎ %K ‎singular values‎ %K ‎weak log-majoriz-ation‎ %K ‎normal matrices‎ %K ‎Hadamard product‎ %R %X ‎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. %U http://bims.iranjournals.ir/article_749_d0230ea9feb008375e5aaf7d3bcab2d4.pdf