{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,22]],"date-time":"2026-08-22T07:14:06Z","timestamp":1787382846592,"version":"3.56.0"},"reference-count":7,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Matrix Anal. Appl."],"published-print":{"date-parts":[[1996,7]]},"abstract":"<jats:p>Following the terminology used by Gohberg, Lancaster, and Rodman, the main results of the paper are as follows. (i) Studying the values of the partial multiplicities of a matrix polynomial $A( \\lambda ) = \\lambda ^2 I + \\lambda C + K$ with hermitian coefficients at real eigenvalues $\\lambda _0 $ and determining sharp bounds for the highest degree d of the factor $( \\lambda - \\lambda _0 )^d $ in the bivariate polynomial $t ( \\lambda ,\\epsilon ) = \\det(A ( \\lambda ) + \\lambda \\in C)$. (ii) Finding conditions on general matrices C and K implying that the leading exponent in the Puiseux expansion of the zero $\\lambda ( \\epsilon )$ of $t( \\lambda ,\\epsilon ) = 0$ near $\\lambda _0 $ is $1 \/ a$, where a is the algebraic multiplicity of $\\lambda _0 $.<\/jats:p>","DOI":"10.1137\/s0895479895273608","type":"journal-article","created":{"date-parts":[[2005,2,27]],"date-time":"2005-02-27T07:15:07Z","timestamp":1109488507000},"page":"563-569","source":"Crossref","is-referenced-by-count":4,"title":["On Eigenvalues of Quadratic Matrix Polynomials and Their Perturbations"],"prefix":"10.1137","volume":"17","author":[{"given":"M.","family":"Radjabalipour","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"A.","family":"Salemi","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2012,2,17]]},"reference":[{"key":"R1","unstructured":"Hellmut Baumg\u00e4rtel, Analytic perturbation theory for matrices and operators, Mathematische Lehrb\u00fccher und Monographien, II. Abteilung: Mathematische Monographien [Mathematical Textbooks and Monographs, Part II: Mathematical Monographs], Vol. 64, Akademie-Verlag, Berlin, 1984, 427\u201387c:47022"},{"key":"R2","volume-title":"Matrix polynomials","author":"Gohberg I.","year":"1982"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1016\/0196-8858(86)90036-9"},{"key":"R4","volume-title":"The theory of matrices","author":"Lancaster Peter","year":"1985"},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1137\/0613031"},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1007\/BF01208352"},{"key":"R7","doi-asserted-by":"crossref","DOI":"10.1515\/9783112717912","volume-title":"Theorie der Losungsverzweigung bei nichtlinearen Gleichungen","author":"Wainberg M. M.","year":"1973"}],"container-title":["SIAM Journal on Matrix Analysis and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/S0895479895273608","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T13:48:09Z","timestamp":1787320089000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/S0895479895273608"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1996,7]]},"references-count":7,"journal-issue":{"issue":"3","published-print":{"date-parts":[[1996,7]]}},"alternative-id":["10.1137\/S0895479895273608"],"URL":"https:\/\/doi.org\/10.1137\/s0895479895273608","relation":{},"ISSN":["0895-4798","1095-7162"],"issn-type":[{"value":"0895-4798","type":"print"},{"value":"1095-7162","type":"electronic"}],"subject":[],"published":{"date-parts":[[1996,7]]}}}