
Eigenvalue Problem
I'm given three matrices: $\displaystyle M_1$, $\displaystyle M_2$ and $\displaystyle M_3$, satisfying commutation relations (Einstein summation)
$\displaystyle [M_i,M_j]=i\epsilon_{ijk}M_k$.
Eigenvalues of $\displaystyle M_3$ and their degeneracy is known and I need to find eigenvalues and degeneracies of $\displaystyle M^2\equiv M_1^2+M_2^2+M_3^2$.
I found that $\displaystyle M^2$ and $\displaystyle M_3$ commute, so they have common set of eigenvectors (but there are also degenerate vectors).
I don't really know how to start, so any tips are appreciated. Thanks in advance!