= Steady states of an affine Bloch equation
{title2=$As_*=-c$}
An arbitrary real affine equation has <steady states> exactly when $\operatorname{rank}A=\operatorname{rank}[A\mid-c]$. Its solution set is $s_*+\ker A$. For a finite-dimensional time-independent <Lindblad equation>, physical stationary states always exist by time averaging trajectories. If $A$ is invertible the <steady state> is unique. Conversely, a nonzero traceless Hermitian stationary direction can be decomposed into the difference of two equally weighted <density operators>; time averaging their trajectories yields two distinct stationary <density operators>. Thus singularity of the physical Bloch matrix also obstructs physical uniqueness.
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