21. Norm preservers of Jordan productsBojan 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: 3261; Downloads: 228
 Link to full text |
22. Zhang, Xian; Sze, Nung-Sing: Additive rank-one preservers between spaces of rectangular matrices. (English). - [J] Linear Multilinear Algebra 53, No. 6, 417-425 (2005). [ISSN 0308-1087; ISSN 1563-5139]Bojan Kuzma, 2006, review, book review, critique Keywords: matematika, linearna algebra, prostor matrik, rank 1, aditivni ohranjevalec
Published in RUP: 15.10.2013; Views: 3513; Downloads: 45
Link to full text |
23. Fosner, Ajda; Šemrl, Peter: Additive maps on matrix algebras preserving invertibility. (English). - [J] Acta Math. Sin., Engl. Ser. 21, No. 4, 681-684 (2005). [ISSN 1439-8516; ISSN 1439-7617]Bojan Kuzma, 2006, review, book review, critique Keywords: matematika, linearna algebra, aditivna preslikava, ohranjevalec obrnljivosti, ohranjevalec singularnosti, matrična algebra
Published in RUP: 15.10.2013; Views: 3643; Downloads: 40
Link to full text |
24. Rank-permutable additive mappingsAnna A. Alieva, Aleksandr Èmilevič Guterman, Bojan Kuzma, 2006, original scientific article Abstract: Let ▫$\sigma$▫ be a fixed non-identical permutation on ▫$k$▫ elements. Additive bijections ▫$T$▫ on the matrix algebra ▫$M_n(\mathbb{F})$▫ over a field ▫$\mathbb{F}$▫ of characteristic zero, with the property that ▫$\rm{rk} (A_1...A_k) = \rm{rk} (A_{\sigma(1)}...A_{\sigma(k)})$▫ implies the same condition on the ▫$T$▫ images, are characterized. It is also shown that the surjectivity assumption can be relaxed, if this property is preserved in both directions.
Keywords: mathematics, linearna algebra, matrix algebra, rank, permutation, additive preservers
Published in RUP: 15.10.2013; Views: 3451; Downloads: 89
Link to full text |
25. Chebotar, Mikhail A.; Fong, Yuen; Lee, Pjek-Hwee: On maps preserving zeros of the polynomial $xy - yx^ast$. (English). - [J] Linear Algebra Appl. 408, 230-243(2005). [ISSN 0024-3795]Bojan Kuzma, 2006, review, book review, critique Keywords: matematika, linearna algebra, linearni ohranjevalci, funkcijske identitete, matrična algebra
Published in RUP: 15.10.2013; Views: 3611; Downloads: 26
Link to full text |
26. |
27. Zhang, Xian: Linear preservers of rank-sum-maximum, rank, rank-subtractivity, and rank-sum-minimum on symmetric matrices. (English). - [J] Linear Multilinear Algebra 53, No. 3, 153-165 (2005). [ISSN 0308-1087; ISSN 1563-5139]Bojan Kuzma, 2006, review, book review, critique Keywords: matematika, linearna algebra, rang, linearni ohranjevalec, simetrične matrike
Published in RUP: 15.10.2013; Views: 3651; Downloads: 33
Link to full text |
28. Ji, Guoxing; Wu, Baowei: Similarity preserving linear maps on upper triangular matrix algebras. (English). - [J] Linear Algebra Appl. 414, No. 1, 278-287 (2006). [ISSN 0024-3795]Bojan Kuzma, 2006, review, book review, critique Keywords: matematika, linearna algebra, ohranjevalci podobnosti, zgornje trikotne matrike
Published in RUP: 15.10.2013; Views: 3400; Downloads: 39
Link to full text |
