{"ID":2850363,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2510.22393","arxiv_id":"2510.22393","title":"Davis-Kahan Theorem under a moderate gap condition","abstract":"The classical Davis-Kahan theorem provides an efficient bound on the perturbation of eigenspaces of a matrix under a large (eigenvalue) gap condition. In this paper, we consider the case when the gap is moderate. Using a bootstrapping argument, we obtain a new bound which is efficient when the perturbation matrix is uncorrelated to the ground matrix. We believe that this bound is sharp up to a logarithmic term.","short_abstract":"The classical Davis-Kahan theorem provides an efficient bound on the perturbation of eigenspaces of a matrix under a large (eigenvalue) gap condition. In this paper, we consider the case when the gap is moderate. Using a bootstrapping argument, we obtain a new bound which is efficient when the perturbation matrix is un...","url_abs":"https://arxiv.org/abs/2510.22393","url_pdf":"https://arxiv.org/pdf/2510.22393v1","authors":"[\"Phuc Tran\",\"Van Vu\"]","published":"2025-10-25T18:34:49Z","proceeding":"math.NA","tasks":"[\"math.NA\",\"math.SP\",\"math.ST\"]","methods":"[]","has_code":false}