在阅读该页内容之前,我们向量子计算的开创者费曼和Deutsch致敬,同时向三位量子信息学的奠基人Charles H. Bennett, David Deutsch, Peter Shor表示敬意.
问题：
Find the square root and logarithm of the matrix $\left[\begin{array}{ll}4 & 3 \\ 3 & 4\end{array}\right]$ .
求矩阵的平方根与对数.
解答
该矩阵的特征分解为$ \left[\begin{array}{ll}4 & 3 \\ 3 & 4\end{array}\right]=\frac{1}{2}\left[\begin{array}{rr}-1 & 1 \\ 1 & 1\end{array}\right]\left[\begin{array}{ll}1 & 0 \\ 0 & 7\end{array}\right]\left[\begin{array}{rr}-1 & 1 \\ 1 & 1\end{array}\right] $；
平方根为$ \sqrt{M}=\frac{1}{2}\left[\begin{array}{rr}-1 & 1 \\ 1 & 1\end{array}\right]\left[\begin{array}{rr}1 & 0 \\ 0 & \sqrt{7}\end{array}\right]\left[\begin{array}{rr}-1 & 1 \\ 1 & 1\end{array}\right] $;
对数为$ \log (M)=\frac{1}{2}\left[\begin{array}{rr}-1 & 1 \\ 1 & 1\end{array}\right]\left[\begin{array}{rr}0 & 0 \\ 0 & \log (7)\end{array}\right]\left[\begin{array}{rr}-1 & 1 \\ 1 & 1\end{array}\right] $.
参考
[1]www.qtumist.com
参与者
作者：HKL, W65
贡献者:Dingyan, Wjw,Wxw
