Inertia-Sensitive Kreiss Bounds for $J$-Selfadjoint Matrices

What the math gives to ML

The paper gives a dimension-sensitive certificate for transient growth of discrete-time linear dynamics with an indefinite selfadjointness constraint. For a recurrent or state-space layer whose transition matrix satisfies A*J=JA, the usual ambient-dimension factor in the Kreiss bound is replaced by the smaller of the minimal-polynomial degree and twice the smaller inertia index of J. This suggests a structured recurrent layer and a resolvent-based regularizer that directly suppresses nonnormal transient amplification rather than merely penalizing eigenvalue magnitude. The main practical opportunity is improved long-horizon stability at fixed state size, although the spectral-disk and resolvent conditions must be estimated numerically.