论文信息 - The Frobenius norm and the commutator

The Frobenius norm and the commutator

In an earlier paper we conjectured an inequality for the Frobenius norm of the commutator of two matrices. This conjecture was recently proved by Seak-Weng Vong and Xiao-Qing Jin and independently also by Zhiqin Lu. We here give a completely different proof of this inequality, prove some related results, and embark on the corresponding question for unitarily invariant norms.

Albrecht Böttcher | David Wenzel | A. Böttcher | David Wenzel

[1] Xiao-Qing Jin,et al. Proof of Böttcher and Wenzel's Conjecture , 2008 .

[2] Charles R. Johnson,et al. Matrix analysis , 1985, Statistical Inference for Engineers and Data Scientists.

[3] Albrecht Böttcher,et al. How big can the commutator of two matrices be and how big is it typically , 2005 .

[4] Zhiqin Lu. Proof of the normal scalar curvature conjecture , 2007, 0711.3510.

[5] Anthony M. Bloch,et al. Commutators of Skew-Symmetric Matrices , 2005, Int. J. Bifurc. Chaos.

[6] R. Bhatia,et al. Commutators, pinchings, and spectral variation , 2008 .

[7] L. László. Proof of Böttcher and Wenzel’s conjecture on commutator norms for 3-by-3 matrices , 2007 .