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Davis–Kahan theorem under a moderate gap condition

Year: 2025

Type: article

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. By 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.

Source: Communications in Contemporary Mathematics

DOI: 10.1142/s021919972550035x

Authors: Phuc Tran, Van Vu

Institution: Yale University

Language: English

Topic: Matrix Theory and Algorithms

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, Simons Foundation

OpenAlex ID: W4408935951

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