= Instantaneous energy-growth criterion for a linear system
For $x'=Lx$ and $E=\|x\|_2^2$, the <Hermitian matrix> $H=(L+L^*)/2$ gives $\dot E=2x^*Hx$. Thus some initial condition grows immediately iff the largest <eigenvalue> of $H$ is positive. All trajectories have nonincreasing energy iff $H$ is a <negative semidefinite matrix>. This differs from requiring negative real parts for the <eigenvalues> of $L$: a <non-normal matrix> can satisfy modal decay while allowing <transient growth>.
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