Open Research Index

Yu-Wang-Samworth 2015: population-gap eigenspace and singular-subspace perturbation bounds

Jon Crall, Edward Wang

Palomar Registrypalomar/PALOMAR-2026-09-18-000005Sep 18, 2026math.STscore 0

A machine-checked Lean 4 formalization of the principal population-gap perturbation results of Yi Yu, Tengyao Wang and Richard J. Samworth, "A useful variant of the Davis-Kahan theorem for statisticians" (Biometrika 102 (2015) 315-323). This single Palomar entry compares both conclusions of Theorem 2 and both displays of Corollary 1 for eigenspaces of real symmetric matrices, together with the right- and left-singular-subspace conclusions of Theorem 3 for general real matrices and two supporting equivalences between its Gram-eigenvector formulation and the paper's paired singular-vector…

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