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1.
On maximal distances in a commuting graph
Gregor Dolinar, Bojan Kuzma, Polona Oblak, 2012, original scientific article

Abstract: It is shown that matrices over algebraically closed fields that are farthest apart in the commuting graph must be non-derogatory. Rank-one matrices and diagonalizable matrices are also characterized in terms of the commuting graph.
Keywords: matematika, linearna algebra, teorija grafov, komutirajoči grafi, matrična algebra, algebraično zaprt obseg, centralizator, razdalja v grafih, mathematics, linear algebra, graph theory, commuting graph, matrix algebra, algebraically closed field, centralizer, distance in graphs
Published in RUP: 03.04.2017; Views: 2228; Downloads: 256
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2.
Norm preservers of Jordan products
Bojan Kuzma, Gorazd Lešnjak, Chi-Kwong Li, Tatjana Petek, Leiba Rodman, 2011, original scientific article

Abstract: V članku klasificiramo surjektivne preslikave, ki na algebri kompleksnih matrik ohranjajo Frobeniusovo normo Jordanskega produkta. Izkaže se, da so do unitarne podobnosti in množenja s skalarnim večkratnikom vse tovrstne preslikave le štirih možnih tipov: (i) preslikava, ki je lokalno adjungiranje na normalnih matrikah in identiteta izven normalnih matrik, (ii) transponiranje, (iii) kompleksna konjugacija in (iv) adjungiranje. Do podobnih zaključkov pridemo tudi v primeru nekaterih drugih unitarno invariantnih norm, kjer pokažemo, da preslikava bodisi normalne matrike množi s skalarji, bodisi jih adjungira in množi s skalarji.
Keywords: matematika, linearna algebra, jordanski produkt, matrična norma, ohranjevalci
Published in RUP: 15.10.2013; Views: 3153; Downloads: 227
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