= Octet and singlet in a fundamental SU3 tensor product
{title2=$\mathbf3\otimes\overline{\mathbf3}=\mathbf8\oplus\mathbf1$}
The <tensor-product weight diagram> has six distinct nonzero differences of the three defining weights and a zero weight of multiplicity three. Identify the tensor product with endomorphisms of $\mathbb C^3$ under conjugation. Its scalar line is a singlet, while the traceless matrices give the irreducible adjoint octet, with two zero weights. The root <commutators> connect all of the traceless matrix units, proving irreducibility rather than inferring it solely from a drawing.
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