A short note on the Frobenius norm of the commutator |
| |
Authors: | Yan-Dong Wu Xu-Qing Liu |
| |
Institution: | 1. Huaiyin Institute of Technology, Huaiyin, China
|
| |
Abstract: | This note mainly aims to improve the inequality, proposed by Böttcher and Wenzel, giving the upper bound of the Frobenius norm of the commutator of two particular matrices in ? n×n . We first propose a new upper bound on basis of the Böttcher and Wenzel’s inequality. Motivated by the method used, the inequality ‖XY ? XY‖ F 2 ≤ 2‖X‖ F 2 ‖Y‖ F 2 is finally improved into $$ \left\| {XY - YX} \right\|_F^2 \leqslant 2\left\| X \right\|_F^2 \left\| Y \right\|_F^2 - 2tr(X^T Y)]^2 . $$ . In addition, a further improvement is made. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|