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A survey on the böttcher-wenzel conjecture and related problems
CHE-MAN CHENG; XIAO-QING JIN; SEAK-WENG VONG
2015
Source PublicationOperators and Matrices
ISSN1846-3886
Volume9Issue:3Pages:659-673
Abstract

A fundamental fact in matrix theory is that the matrix multiplication is not commutative, i.e., there are square matrices X and Y such that XY≠YX. The difference XY — YX is called the commutator (or Lie product) of X and Y. The commutator plays an important role in diverse areas in mathematics, for instance, Lie group and Lie algebra theory, perturbation analysis, and matrix manifold computation. Bottcher and Wenzel proposed the following conjecture in 2005: for any real n x n matrices X and Y, ║XY-YX║F ≤√2 ║X║F║Y║X║F. where ║ ║F is the Frobenius norm. This survey is concerned with the proofs of this conjecture and the study of its related problems.

KeywordBöttcher-wenzel Conjecture Commutator Of Two Matrices Frobenius Norm
DOIhttp://doi.org/10.7153/oam-09-39
URLView the original
Indexed BySCI
Language英语
WOS Research AreaMathematics
WOS SubjectMathematics
WOS IDWOS:000369439800010
PublisherELEMENT
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Citation statistics
Cited Times [WOS]:3   [WOS Record]     [Related Records in WOS]
Document TypeJournal article
CollectionDEPARTMENT OF MATHEMATICS
Corresponding AuthorCHE-MAN CHENG; XIAO-QING JIN; SEAK-WENG VONG
AffiliationUniversidade de Macau
Recommended Citation
GB/T 7714
CHE-MAN CHENG,XIAO-QING JIN,SEAK-WENG VONG. A survey on the böttcher-wenzel conjecture and related problems[J]. Operators and Matrices,2015,9(3):659-673.
APA CHE-MAN CHENG,XIAO-QING JIN,&SEAK-WENG VONG.(2015).A survey on the böttcher-wenzel conjecture and related problems.Operators and Matrices,9(3),659-673.
MLA CHE-MAN CHENG,et al."A survey on the böttcher-wenzel conjecture and related problems".Operators and Matrices 9.3(2015):659-673.
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