Eigenvalues of Circulant Matrices and Rank-One Perturbations: A Survey

Eigenvalues of Circulant Matrices and Rank-One Perturbations: A Survey | Authorea try { document.documentElement.classList.add('js'); } catch (e) { } var _gaq = _gaq || []; _gaq.push(['_setAccount', 'G-8VDV14Y67G']); _gaq.push(['_trackPageview']); (function() { var ga = document.createElement('script'); ga.type = 'text/javascript'; ga.async = true; ga.src = ('https:' == document.location.protocol ? 'https://ssl' : 'http://www') + '.google-analytics.com/ga.js'; var s = document.getElementsByTagName('script')[0]; s.parentNode.insertBefore(ga, s); })(); Skip to main content Preprints Collections Wiley Open Research IET Open Research Ecological Society of Japan All Collections About About Authorea FAQs Contact Us Quick Search anywhere Search for preprint articles, keywords, etc. Search Search ADVANCED SEARCH SCROLL This is a preprint and has not been peer reviewed. Data may be preliminary. 14 January 2026 V1 Latest version Share on Eigenvalues of Circulant Matrices and Rank-One Perturbations: A Survey Author : Ishpreet Kaur 0009-0001-0065-7024 [email protected] Authors Info & Affiliations https://doi.org/10.22541/au.176843180.05019719/v1 101 views 47 downloads Contents Abstract Supplementary Material Information & Authors Metrics & Citations View Options References Figures Tables Media Share Abstract Circulant matrices form an important class of structured matrices whose spectral properties can be described explicitly using the discrete Fourier transform. In this survey, we review the eigenvalue structure of circulant matrices with real entries and examine how rank-one perturbations affect their spectra. A simple illustrative example is included to demonstrate the stability and variation of eigenvalues under low-rank modifications. Supplementary Material File (eigenvalues_of_circulant_matrices_and_rank_one_perturbations__a_survey (12).pdf) Download 191.49 KB Information & Authors Information Version history V1 Version 1 14 January 2026 Copyright This work is licensed under a Creative Commons Attribution 4.0 International License Keywords circulant matrix eigen values perturbed matrices rank one perturbed spectral theory Authors Affiliations Ishpreet Kaur 0009-0001-0065-7024 [email protected] View all articles by this author Metrics & Citations Metrics Article Usage 101 views 47 downloads .FvxKWukQNSOunydq8rnd { width: 100px; } Citations Download citation Ishpreet Kaur. Eigenvalues of Circulant Matrices and Rank-One Perturbations: A Survey. Authorea . 14 January 2026. DOI: https://doi.org/10.22541/au.176843180.05019719/v1 If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. 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