We propose a generalization of the Filoche-Mayboroda localization landscape that extends the theory well beyond the static, elliptic, and Hermitian settings while preserving its geometric interpretability and recovering the original framework as a special case. Using the positive operator $H^{†}H$, we obtain a geometric diagnostic of localization without computing any eigenstate. Singular-value collapse reveals spectral instabilities and the skin-effect geometry associated with right-eigenstate accumulation. In driven systems, we establish a precise connection between near-gap closings in the singular-value spectrum of the Sambe operator and dynamical localization. The Sambe formulation captures coherent destruction of tunneling, while topological zero modes are accurately identified in both one- and two-dimensional models. Benchmarks on Hatano-Nelson chains, driven two-level systems, and driven Aubry-André-Harper models confirm quantitative accuracy. The resulting framework provides a focused geometric diagnostic for singular non-Hermitian and Floquet physics, with favorable computational scaling for multifrequency driven systems.

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• Anderson localization
• Cold atoms & matter waves
• Topological insulators
• Floquet systems
• Non-Hermitian systems
• Exact diagonalization
• Tight-binding model