= Hamiltonian rotations of Bloch vectors
{c}
{title2=$\dot s=As,\quad A^T=-A$}
In a Hilbert-Schmidt orthonormal operator basis, the generator $-i[H,\cdot]$ is represented on the traceless Hermitian subspace by a real <skew-symmetric matrix>. Its propagator is therefore in the <special orthogonal group> and preserves the <purity of a density operator>. For $N>2$, these rotations form the adjoint image of the accessible unitary group, generally a proper subgroup of the full Euclidean rotation group; preservation of the full <spectrum> of the <density operator> imposes further constraints.
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