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## Main Question or Discussion Point

For an electron the spin operator [itex]S_z[/itex]is represented by a [itex]2×2[/itex] matrix, with spin up and down as its bases. Consider the angular momentum operator [itex]L_z[/itex] with [itex]l=1[/itex] which is a [itex]3×3[/itex] matrix. How can we treat the [itex]L_z S_z[/itex] operator directly in matrix form?