= Generalized Bloch representation
{c}
{title2=$\rho=I/N+\sum_{k=1}^{N^2-1}s_k\sigma_k$}
Choose a <Hilbert-Schmidt inner product> orthonormal Hermitian operator basis with final element $I/\sqrt N$. A <density operator> has real coefficients $r_k=\operatorname{Tr}(\sigma_k\rho)$ and fixed final coefficient $1/\sqrt N$. The remaining coefficients form its generalized <Bloch vector>. Positivity restricts these real vectors to a compact convex body; for $N>2$ this body is not the entire Euclidean ball allowed by a purity bound.
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