Eigenvalue Equations for Spin-1 System:

    𝐒𝓏|1〉 = ħ|1〉
    𝐒𝓏|0〉 = 0ħ|0〉
    𝐒𝓏|-1〉 = ħ|-1〉

      ħ  ( 1 0 0 )
S𝓏 ≐ --- ( 0 1 0 )
     √2  ( 0 0 1 )

      ħ  ( 0 1 0 )
S𝓍 ≐ --- ( 1 0 1 )
     √2  ( 0 1 0 )

      ħ  ( 0  -ι   0  )
S𝓎 ≐ --- ( ι   0  -ι  )
     √2  ( 0   ι   0  )