On an eigenvalue inequality involving the Hadamard product

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• 作者：Fumio Hiai^a ; ^{hiai.fumio@gmail.com} ; Minghua Lin^b ; ^{m_lin@i.shu.edu.cn}
• 关键词：15A45 ; 15A42
• 刊名：Linear Algebra and its Applications
• 出版年：2017
• 出版时间：15 February 2017
• 年：2017
• 卷：515
• 期：Complete
• 页码：313-320
• 全文大小：242 K
• 卷排序：515

文摘

Let A, B   be n×nn×n positive definite matrices. Then for 0≤t≤10≤t≤1∏i=knλi(A∘B)≥∏i=knλi((A♯tB)(A♯1−tB))≥∏i=knλi(AB),k=1,…,n. This gives a weighted extension of a result of Ando [1]. The case where the eigenvalues λiλi are replaced with the singular values σiσi is also considered.