= Conserved inventory from a left null vector
{title2=$w^TA=0\ \Longrightarrow\ (w^Tc)'=-w^Tb$}
For the <linear ordinary differential equation> $c'=Ac-b$, a fixed <left null space> <vector> gives $(w^Tc)'=-w^Tb$. Thus $w^Tc$ is a <conserved quantity> when $w^Tb=0$. In a <box model> written for <concentrations> per unit <volume>, physical tracer inventory uses the box <volumes> as weights. Zero column sums make $w=\mathbf1$ possible, but that property must be checked rather than assumed.
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