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## Main Question or Discussion Point

When discussing how a rank two tensor transforms under SO(3), we say that the tensor can be decomposed into three irreducible parts, the anti-symmetric part, traceless-symmetric part, and a 1-dimensional trace part, which transforms as a scalar. How do we know that the symmetric and anti-symmetric parts are truly irreducible, i.e. that they cannot be further block diagonalized via some change of basis?