$$$\left[\begin{array}{ccc}0 & \frac{1}{2} & 0\\\frac{\sqrt{2}}{4} & \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{4}\\\frac{\sqrt{2}}{4} & 0 & \frac{\sqrt{2}}{4}\end{array}\right]\cdot \left[\begin{array}{c}\frac{\sqrt{6}}{6}\\\frac{\sqrt{6}}{3}\\\frac{\sqrt{6}}{6}\end{array}\right]$$$

Berechne $$$\left[\begin{array}{ccc}0 & \frac{1}{2} & 0\\\frac{\sqrt{2}}{4} & \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{4}\\\frac{\sqrt{2}}{4} & 0 & \frac{\sqrt{2}}{4}\end{array}\right]\cdot \left[\begin{array}{c}\frac{\sqrt{6}}{6}\\\frac{\sqrt{6}}{3}\\\frac{\sqrt{6}}{6}\end{array}\right].$$$

$$$\left[\begin{array}{ccc}{\color{GoldenRod}0} & {\color{Brown}\frac{1}{2}} & {\color{Fuchsia}0}\\{\color{DarkBlue}\frac{\sqrt{2}}{4}} & {\color{Purple}\frac{\sqrt{2}}{2}} & {\color{Magenta}\frac{\sqrt{2}}{4}}\\{\color{Blue}\frac{\sqrt{2}}{4}} & {\color{Violet}0} & {\color{DarkMagenta}\frac{\sqrt{2}}{4}}\end{array}\right]\cdot \left[\begin{array}{c}{\color{Peru}\frac{\sqrt{6}}{6}}\\{\color{Purple}\frac{\sqrt{6}}{3}}\\{\color{Violet}\frac{\sqrt{6}}{6}}\end{array}\right] = \left[\begin{array}{c}{\color{GoldenRod}\left(0\right)}\cdot {\color{Peru}\left(\frac{\sqrt{6}}{6}\right)} + {\color{Brown}\left(\frac{1}{2}\right)}\cdot {\color{Purple}\left(\frac{\sqrt{6}}{3}\right)} + {\color{Fuchsia}\left(0\right)}\cdot {\color{Violet}\left(\frac{\sqrt{6}}{6}\right)}\\{\color{DarkBlue}\left(\frac{\sqrt{2}}{4}\right)}\cdot {\color{Peru}\left(\frac{\sqrt{6}}{6}\right)} + {\color{Purple}\left(\frac{\sqrt{2}}{2}\right)}\cdot {\color{Purple}\left(\frac{\sqrt{6}}{3}\right)} + {\color{Magenta}\left(\frac{\sqrt{2}}{4}\right)}\cdot {\color{Violet}\left(\frac{\sqrt{6}}{6}\right)}\\{\color{Blue}\left(\frac{\sqrt{2}}{4}\right)}\cdot {\color{Peru}\left(\frac{\sqrt{6}}{6}\right)} + {\color{Violet}\left(0\right)}\cdot {\color{Purple}\left(\frac{\sqrt{6}}{3}\right)} + {\color{DarkMagenta}\left(\frac{\sqrt{2}}{4}\right)}\cdot {\color{Violet}\left(\frac{\sqrt{6}}{6}\right)}\end{array}\right] = \left[\begin{array}{c}\frac{\sqrt{6}}{6}\\\frac{\sqrt{3}}{2}\\\frac{\sqrt{3}}{6}\end{array}\right]$$$

$$$\left[\begin{array}{ccc}0 & \frac{1}{2} & 0\\\frac{\sqrt{2}}{4} & \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{4}\\\frac{\sqrt{2}}{4} & 0 & \frac{\sqrt{2}}{4}\end{array}\right]\cdot \left[\begin{array}{c}\frac{\sqrt{6}}{6}\\\frac{\sqrt{6}}{3}\\\frac{\sqrt{6}}{6}\end{array}\right] = \left[\begin{array}{c}\frac{\sqrt{6}}{6}\\\frac{\sqrt{3}}{2}\\\frac{\sqrt{3}}{6}\end{array}\right]\approx \left[\begin{array}{c}0.408248290463863\\0.866025403784439\\0.288675134594813\end{array}\right]$$$A