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Proof of Bottcher and Wenzel's Conjecture
Seak-Weng Vong; Xiao-Qing Jin
Source PublicationOperators and matrices

In 2005, Bottcher and Wenzel raised a conjecture that if ¨ X and Y are any two real n -by- n matrices, then XY −YX2 F 2X2 FY2 F where ·F denotes the Frobenius norm. They proved this for the case of 2 -by- 2 matrices. Later, Laszl ´ o proved the conjecture for the ´ case of 3 -by- 3 matrices. In this paper, we prove the conjecture for general n -by- n matrices.

KeywordCommutator Of Two Matrices The Cauchy-schwarz Inequality The Lagrange Identity
Indexed BySCI
WOS Research AreaMathematics
WOS SubjectMathematics
WOS IDWOS:000263564100008
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Cited Times [WOS]:22   [WOS Record]     [Related Records in WOS]
Document TypeJournal article
CollectionFaculty of Science and Technology
AffiliationUniversity of Macau
First Author AffilicationUniversity of Macau
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GB/T 7714
Seak-Weng Vong,Xiao-Qing Jin. Proof of Bottcher and Wenzel's Conjecture[J]. Operators and matrices,2008,2(3):435–442.
APA Seak-Weng Vong,&Xiao-Qing Jin.(2008).Proof of Bottcher and Wenzel's Conjecture.Operators and matrices,2(3),435–442.
MLA Seak-Weng Vong,et al."Proof of Bottcher and Wenzel's Conjecture".Operators and matrices 2.3(2008):435–442.
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