标签:style io color os sp for on bs amp
For fixed basis of in $\scrH$ and $\scrK$, the matrix $A^*$ is the conjugate transpose of the matrix of $A$.
Solution. $$\beex \bea (A^*)_{ij}&=e_i^*A^*f_j\\ &=\sef{e_i,A^*f_j}_\scrH\\ &=\sef{Ae_i,f_j}_\scrK\\ &=\overline{\sef{f_j,Ae_i}}\\ &=\overline{a}_{ji}. \eea \eeex$$
[Bhatia.Matrix Analysis.Solutions to Exercises and Problems]ExI.2.1
标签:style io color os sp for on bs amp
原文地址:http://www.cnblogs.com/zhangzujin/p/4105326.html