= Stability matrix
{title2=$J=Df(x_*)$}
For $\dot x=f(x)$ near an <equilibrium point>, the stability matrix is the <Jacobian matrix> of the vector field evaluated at that point. Perturbations obey $\dot\eta=J\eta$ to first order. Its <eigenvalues> determine linear growth and decay: strictly negative real parts imply local <asymptotic stability>, while a positive real part gives instability. Zero real parts require further analysis. The <stability matrix of a renormalization-group fixed point> applies this construction to beta-function flows.
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