{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T16:42:42Z","timestamp":1787330562423,"version":"build-2736575974"},"reference-count":22,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"2","funder":[{"DOI":"10.13039\/501100003329","name":"Ministerio de Econom\u00eda y Competitividad","doi-asserted-by":"publisher","award":["MTM2017-83624-P"],"award-info":[{"award-number":["MTM2017-83624-P"]}],"id":[{"id":"10.13039\/501100003329","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003329","name":"Ministerio de Econom\u00eda y Competitividad","doi-asserted-by":"publisher","award":["MTM2017-90682-REDT"],"award-info":[{"award-number":["MTM2017-90682-REDT"]}],"id":[{"id":"10.13039\/501100003329","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004233","name":"Universitat Polit\u00e8cnica de Val\u00e8ncia","doi-asserted-by":"publisher","award":["GIU16\/42"],"award-info":[{"award-number":["GIU16\/42"]}],"id":[{"id":"10.13039\/501100004233","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Matrix Anal. Appl."],"published-print":{"date-parts":[[2019,1]]},"abstract":"<jats:p>We solve the problem of determining the Weierstrass structure of a regular matrix pencil obtained by a low rank perturbation of another regular matrix pencil. We apply the result to find necessary and sufficient conditions for the existence of a low rank perturbation such that the perturbed pencil has prescribed eigenvalues and algebraic multiplicities. The results hold over fields with sufficient number of elements.<\/jats:p>","DOI":"10.1137\/18m1200245","type":"journal-article","created":{"date-parts":[[2019,4,16]],"date-time":"2019-04-16T13:16:05Z","timestamp":1555420565000},"page":"440-453","source":"Crossref","is-referenced-by-count":10,"title":["Weierstrass Structure and Eigenvalue Placement of Regular Matrix Pencils under Low Rank Perturbations"],"prefix":"10.1137","volume":"40","author":[{"given":"Itziar","family":"Baragan\u0342a","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Alicia","family":"Roca","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2019,4,16]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1016\/j.laa.2014.06.041"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.13001\/1081-3810.2014"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1137\/060659922"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1137\/15M1022069"},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.1137\/050633020"},{"key":"atypb6","doi-asserted-by":"publisher","DOI":"10.1016\/j.laa.2014.05.029"},{"key":"atypb7","doi-asserted-by":"crossref","unstructured":"S. Friedland,\n                      Matrices-Algebra, Analysis and Applications\n                      , World Scientific, Hackensack, NJ, 2016.","DOI":"10.1142\/9567"},{"key":"atypb8","unstructured":"F. Gantmacher,\n                      Matrix Theory\n                      , Vols. I, II, Chelsea, New York, 1974."},{"key":"atypb9","doi-asserted-by":"publisher","DOI":"10.1137\/16M1066877"},{"key":"atypb10","doi-asserted-by":"crossref","unstructured":"M. K. I. Gohberg and F. van Schagen,\n                      Partially Specified Matrices and Operators: Classification, Completion, Applications\n                      , Birkh\u00e4user Verlag, Basel, 1995.","DOI":"10.1007\/978-3-0348-9100-4"},{"key":"atypb11","unstructured":"L. Leiben, F. Mart\u00ednez Per\u00eda, F. Philipp, C. Trunk, H. Winkler,\n                      Finite Rank Perturbations of Linear Relations and Singular Matrix Pencils\n                      , preprint,https:\/\/arxiv.org\/abs\/1806.07513, 2018."},{"key":"atypb12","doi-asserted-by":"publisher","DOI":"10.13001\/1081-3810.1313"},{"key":"atypb13","unstructured":"E. Marques de S\u00e0,\n                      Imersa\u0342o de matrices e entrela\u00e7amento de factores invariantes\n                      , Ph.D. thesis, University of Coimbra, Coimbra, Portugal, 1979."},{"key":"atypb14","doi-asserted-by":"publisher","DOI":"10.1016\/j.laa.2010.07.025"},{"key":"atypb15","doi-asserted-by":"publisher","DOI":"10.1137\/S0895479802417118"},{"key":"atypb16","unstructured":"A. Roca,\n                      Asignaci\u00f3n de Invariantes en Sistemas de Control\n                      , Ph.D. thesis, Universitat Polit\u00e8cnica Val\u00e8ncia, Val\u00e8ncia, Spain, 2003."},{"key":"atypb17","doi-asserted-by":"publisher","DOI":"10.1023\/A:1026104129373"},{"key":"atypb18","doi-asserted-by":"publisher","DOI":"10.1023\/B:FAIA.0000024871.00388.4c"},{"key":"atypb19","doi-asserted-by":"publisher","DOI":"10.1080\/03081088808817898"},{"key":"atypb20","doi-asserted-by":"publisher","DOI":"10.1080\/03081088808817897"},{"key":"atypb21","doi-asserted-by":"publisher","DOI":"10.4153\/CJM-1980-018-9"},{"key":"atypb22","doi-asserted-by":"publisher","DOI":"10.1137\/0612003"}],"container-title":["SIAM Journal on Matrix Analysis and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/18M1200245","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T16:12:34Z","timestamp":1787328754000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/18M1200245"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,1]]},"references-count":22,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2019,1]]}},"alternative-id":["10.1137\/18M1200245"],"URL":"https:\/\/doi.org\/10.1137\/18m1200245","relation":{},"ISSN":["0895-4798","1095-7162"],"issn-type":[{"value":"0895-4798","type":"print"},{"value":"1095-7162","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,1]]}}}