{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/inference-on-eigenvectors-of-non-symmetric","title":"Hypothesis testing on invariant subspaces of non-symmetric matrices with applications to network statistics","arxiv_id":"2303.18233","date":"2023-03-31","proceeding":null,"authors":["Jérôme R. Simons"],"abstract":"We extend the inference procedure for eigenvectors of Tyler (1981), which assumes symmetrizable matrices to generic invariant and singular subspaces of non-diagonalisable matrices to test whether $\\nu \\in \\mathbb{R}^{p \\times r}$ is an element of an invariant subspace of $M \\in \\mathbb{R}^{p \\times p}$. Our results include a Wald test for full-vector hypotheses and a $t$-test for coefficient-wise hypotheses. We employ perturbation expansions of invariant subspaces from Sun (1991) and singular subspaces from Liu et al. (2007). Based on the former, we extend the popular Davis-Kahan bound to estimations of its higher-order polynomials and study how the bound simplifies for eigenspaces but attains complexity for generic invariant subspaces.","url_abs":"https://arxiv.org/abs/2303.18233v4","url_pdf":"https://arxiv.org/pdf/2303.18233v4.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"inference-on-eigenvectors-of-non-symmetric","repo_url":"https://github.com/jsimons8/networkmodelssubspaces","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[{"method_slug":"test","method_name":"Test"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}