| Residential College | false |
| Status | 已發表Published |
| Another Proof for Commutators with Maximal Frobenius Norm | |
Che-man Cheng ; Kin-sio Fong ; Io-kei Lok
| |
| 2011 | |
| Source Publication | Recent Advances in Scientific Computing and Matrix Analysis |
| Publisher | International Press |
| Pages | 9-14 |
| Abstract | It has been proved that for all n×n complex matrices X and Y, ∥XY-YX∥ F ≤2∥X∥ F ∥Y∥ F , where ∥·∥ F denotes the Frobenius norm. A characterization of those pairs of matrices that satisfy the corresponding equality ∥XY-YX∥ F =2∥X∥ F ∥Y∥ F has also been found. Recently, K. M. R. Audenaert [Linear Algebra Appl. 432, No. 5, 1126–1143 (2010; Zbl 1194.60020)] has given a new proof of the inequality by introducing a matrix version of variance. In this paper, based on his proof, we give another proof for the characterization of the matrices that attain the above equality. |
| Language | 英語English |
| ISBN | 978-1571462022 |
| Document Type | Book chapter |
| Collection | Faculty of Science and Technology DEPARTMENT OF MATHEMATICS |
| Affiliation | Department of Mathematics, University of Macau, Macao, China |
| First Author Affilication | University of Macau |
| Recommended Citation GB/T 7714 | Che-man Cheng,Kin-sio Fong,Io-kei Lok. Another Proof for Commutators with Maximal Frobenius Norm[M]. Recent Advances in Scientific Computing and Matrix Analysis:International Press, 2011, 9-14. |
| APA | Che-man Cheng., Kin-sio Fong., & Io-kei Lok (2011). Another Proof for Commutators with Maximal Frobenius Norm. Recent Advances in Scientific Computing and Matrix Analysis, 9-14. |
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