{"?xml":{"@version":"1.0"},"edm:RDF":{"@xmlns:dc":"http://purl.org/dc/elements/1.1/","@xmlns:edm":"http://www.europeana.eu/schemas/edm/","@xmlns:wgs84_pos":"http://www.w3.org/2003/01/geo/wgs84_pos","@xmlns:foaf":"http://xmlns.com/foaf/0.1/","@xmlns:rdaGr2":"http://rdvocab.info/ElementsGr2","@xmlns:oai":"http://www.openarchives.org/OAI/2.0/","@xmlns:owl":"http://www.w3.org/2002/07/owl#","@xmlns:rdf":"http://www.w3.org/1999/02/22-rdf-syntax-ns#","@xmlns:ore":"http://www.openarchives.org/ore/terms/","@xmlns:skos":"http://www.w3.org/2004/02/skos/core#","@xmlns:dcterms":"http://purl.org/dc/terms/","edm:WebResource":[{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-Y1D9CTOL/49af6f3d-520e-42c8-a8b7-4f9a93de6504/PDF","dcterms:extent":"285 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-Y1D9CTOL/7b552de5-0d1f-48f1-b193-080c6888c919/TEXT","dcterms:extent":"18 KB"}],"edm:TimeSpan":{"@rdf:about":"2008-2025","edm:begin":{"@xml:lang":"en","#text":"2008"},"edm:end":{"@xml:lang":"en","#text":"2025"}},"edm:ProvidedCHO":{"@rdf:about":"URN:NBN:SI:doc-Y1D9CTOL","dcterms:isPartOf":[{"@rdf:resource":"https://www.dlib.si/details/URN:NBN:SI:spr-UP1WMFAR"},{"@xml:lang":"sl","#text":"Ars mathematica contemporanea"}],"dcterms:issued":"2021","dc:creator":"Costara, Constantin","dc:format":[{"@xml:lang":"sl","#text":"številka:1"},{"@xml:lang":"sl","#text":"letnik:21"},{"@xml:lang":"sl","#text":"str. 125-132"}],"dc:identifier":["DOI:10.26493/1855-3974.2488.f5c","COBISSID_HOST:111792387","ISSN:1855-3966","URN:URN:NBN:SI:doc-Y1D9CTOL"],"dc:language":"en","dc:publisher":{"@xml:lang":"sl","#text":"Univerza na Primorskem, Fakulteta za matematiko, naravoslovje in informacijske tehnologije"},"dc:subject":[{"@xml:lang":"sl","#text":"elementarne simetrične funkcije"},{"@xml:lang":"en","#text":"elementary symmetric function"},{"@xml:lang":"sl","#text":"nelinearen"},{"@xml:lang":"en","#text":"nonlinear"},{"@xml:lang":"sl","#text":"ohranjevalec"},{"@xml:lang":"en","#text":"preserver"}],"dcterms:temporal":{"@rdf:resource":"2008-2025"},"dc:title":{"@xml:lang":"sl","#text":"Nonlinear maps preserving the elementary symmetric functions|"},"dc:description":[{"@xml:lang":"sl","#text":"Let ?$\\mathcal{M}_n$? be the algebra of all ?$n \\times n$? complex matrices, and for a natural number ?$2 \\le k \\le n$? denote by ?$Ek(x)$? the ?$k$?th elementary symmetric function on the eigenvalues of ?$x \\in \\mathcal{M}_n$?. For two maps ?$\\varphi,\\psi \\colon \\mathcal{M}_n \\to \\mathcal{M}_n$?, one of them being surjective, we prove that if ?$E_k(\\lambda x + y) = E_k(\\lambda \\varphi(x) + \\psi(y))$? for each ?$\\lambda \\in C$? and ?$x, y \\in \\mathcal{M}_n$?, then ?$\\varphi =\\ psi$? on ?$\\mathcal{M}_n$?, the common value being a linear map from ?$\\mathcal{M}_n$? into itself. In particular, for ?$3 \\le k \\le n$? the general form of ?$\\varphi$? and ?$\\psi$? can be computed explicitly"},{"@xml:lang":"sl","#text":"Naj bo ?$\\mathcal{M}_n$? algebra vseh kompleksnih matrik velikosti ?$n \\times n$?; za naravno število ?$2 \\le k \\le n$? označimo z ?$Ek(x)$? ?$k$?-to elementarno simetrično funkcijo na lastnih vrednostih matrike ?$x \\in \\mathcal{M}_n$?. Za dve preslikavi ?$\\varphi,\\psi \\colon \\mathcal{M}_n \\to \\mathcal{M}_n$?, pri čemer je ena od njiju surjektivna, dokažemo, da, če je ?$E_k(\\lambda x + y) = E_k(\\lambda \\varphi(x) + \\psi(y))$? za vsak ?$\\lambda \\in C$? in ?$x, y \\in \\mathcal{M}_n$?, velja ?$\\varphi =\\ psi$? na ?$\\mathcal{M}_n$?, pri čemer je ta skupna vrednost linearna preslikava množice ?$\\mathcal{M}_n$? vase. Posebej, za ?$3 \\le k \\le n$?, lahko splošno obliko ?$\\varphi$? in ?$\\psi$? izračunamo eksplicitno"}],"edm:type":"TEXT","dc:type":[{"@xml:lang":"sl","#text":"znanstveno časopisje"},{"@xml:lang":"en","#text":"journals"},{"@rdf:resource":"http://www.wikidata.org/entity/Q361785"}]},"ore:Aggregation":{"@rdf:about":"http://www.dlib.si/?URN=URN:NBN:SI:doc-Y1D9CTOL","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:doc-Y1D9CTOL"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:doc-Y1D9CTOL/49af6f3d-520e-42c8-a8b7-4f9a93de6504/PDF"},"edm:rights":{"@rdf:resource":"http://creativecommons.org/licenses/by/4.0/"},"edm:provider":"Slovenian National E-content Aggregator","edm:intermediateProvider":{"@xml:lang":"en","#text":"National and University Library of Slovenia"},"edm:dataProvider":{"@xml:lang":"sl","#text":"Univerza na Primorskem, Fakulteta za naravoslovje, matematiko in informacijske tehnologije"},"edm:object":{"@rdf:resource":"http://www.dlib.si/streamdb/URN:NBN:SI:doc-Y1D9CTOL/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:doc-Y1D9CTOL"}}}}