= Generalized Pauli matrix
{title2=$\operatorname{Tr}(\sigma_k\sigma_\ell)=\delta_{k\ell}$}
A traceless <Hermitian matrix> in a <Hilbert-Schmidt inner product> orthonormal basis of the real vector space of traceless Hermitian $N$-by-$N$ matrices. One choice uses symmetric and imaginary antisymmetric off-diagonal matrix units, normalized by $1/\sqrt2$, and traceless diagonal generators. Together with $I/\sqrt N$ they form an orthonormal basis of all Hermitian matrices. The coordinates $s_k=\operatorname{Tr}(\rho\sigma_k)$ give the <Generalized Bloch representation>.
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