{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T18:29:13Z","timestamp":1787336953613,"version":"build-2736575974"},"reference-count":13,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Matrix Anal. Appl."],"published-print":{"date-parts":[[2003,1]]},"abstract":"<jats:p>Let A be a matrix and $\\lambda_0$ be one of its eigenvalues having g elementary Jordan blocks in the Jordan canonical form of A. We show that for most matrices B satisfying ${\\rm rank}\\,(B)\\leq g$, the Jordan blocks of A+B with eigenvalue $\\lambda_0$ are just the $g-{\\rm rank}\\,(B)$ smallest Jordan blocks of A with eigenvalue $\\lambda_0$. The set of matrices for which this behavior does not happen is explicitly characterized through a scalar determinantal equation involving B and some of the $\\lambda_0$-eigenvectors of A. Thus, except for a set of zero Lebesgue measure, a low rank perturbation A+B of A destroys for each of its eigenvalues exactly the rank,(B) largest Jordan blocks of A, while the rest remain unchanged.<\/jats:p>","DOI":"10.1137\/s0895479802417118","type":"journal-article","created":{"date-parts":[[2003,10,11]],"date-time":"2003-10-11T19:55:33Z","timestamp":1065902133000},"page":"495-506","source":"Crossref","is-referenced-by-count":46,"title":["Low Rank Perturbation of Jordan Structure"],"prefix":"10.1137","volume":"25","author":[{"given":"Julio","family":"Moro","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Froil\u00e1n M.","family":"Dopico","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,7,31]]},"reference":[{"key":"R1","unstructured":"H. Baumg\u00e4rtel, Analytic perturbation theory for matrices and operators, Operator Theory: Advances and Applications, Vol. 15, Birkh\u00e4user Verlag, 1985, 427\u2013088a:47016"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511810817"},{"key":"R3","unstructured":"C.\u2010P. Jeannerod,\n                      On some nongeneric perturbations of an arbitrary Jordan structure\n                      , Linear Algebra Appl., to appear."},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-66282-9"},{"key":"R5","first-page":"52","volume":"6","author":"Lidski V.","year":"1966","journal-title":". Vy\u010disl. Mat. i Mat. Fiz."},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1016\/S0024-3795(98)90129-X"},{"key":"R7","doi-asserted-by":"publisher","DOI":"10.1137\/S0895479895294666"},{"key":"R8","unstructured":"Julio Moro, Froil\u00e1n Dopico, First order eigenvalue perturbation theory and the Newton diagram, Kluwer\/Plenum, New York, 2003, 143\u20131751966867"},{"key":"R9","unstructured":"S. Savchenko,\n                      The typical change of the spectral properties under a rank one perturbation\n                      , Mat. Zametki, submitted (in Russian)."},{"key":"R10","unstructured":"S. Savchenko,\n                      On the Change of the Spectral Properties under a Generic Perturbation of Rank r\n                      , preprint (in Russian)."},{"key":"R11","volume-title":"Matrix perturbation theory","author":"Stewart G.","year":"1990"},{"key":"R12","doi-asserted-by":"publisher","DOI":"10.1070\/RM1960v015n03ABEH004092"},{"key":"R12","doi-asserted-by":"publisher","DOI":"10.1070\/RM1960v015n03ABEH004092"}],"container-title":["SIAM Journal on Matrix Analysis and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/S0895479802417118","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T17:38:07Z","timestamp":1787333887000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/S0895479802417118"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2003,1]]},"references-count":13,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2003,1]]}},"alternative-id":["10.1137\/S0895479802417118"],"URL":"https:\/\/doi.org\/10.1137\/s0895479802417118","relation":{},"ISSN":["0895-4798","1095-7162"],"issn-type":[{"value":"0895-4798","type":"print"},{"value":"1095-7162","type":"electronic"}],"subject":[],"published":{"date-parts":[[2003,1]]}}}