Theses are angular momentum operator. We will discuss them with details later.
\(L_x = \frac{\hbar}{2} \begin{pmatrix} 0 & \sqrt{2} & 0\\\sqrt{2} & 0 & \sqrt{2}\\0 & \sqrt{2} & 0 \end{pmatrix}\)
\(L_y = \frac{\hbar}{2i} \begin{pmatrix} 0 & \sqrt{2} & 0\\-\sqrt{2} & 0 & \sqrt{2}\\0 & -\sqrt{2} & 0 \end{pmatrix}\)
\(L_y = \hbar \begin{pmatrix} 1 & 0 & 0\\0 & 0 & 0\\0 & 0 & -1 \end{pmatrix}\)
Show commutator of \(L_x\) and \(L_y\), \([L_x, L_y] = i\hbar L_z\).
