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Title:Ob otobraženijah, sohranjajuščih immananty
Authors:Kuzma, Bojan (Author)
Files:URL http://mi.mathnet.ru/rus/fpm/v13/i4/p113
 
Language:Russian
Work type:Not categorized
Tipology:1.01 - Original Scientific Article
Organization:IAM - Andrej Marušič Institute
Abstract:V članku študiramo preslikave, ki transformirajo eno imananto matričnih snopov v drugo. Vnaprej ne predpostavimo niti surjektivnosti, niti linearnosti preslikav. Predpostavimo zgolj šibko linearnost v obliki identitete ▫$d_chi (Phi(A) + lambda Phi(B)) = d_{chi'}(A+lambda B)$▫. Pokažemo, da zgolj ta identiteta implicira avtomatično linearnost in bijektivnost preslikave ▫$Phi$▫.
Keywords:matematika, linearna algebra, teorija matrik, imanante, ohranjevalci
Year of publishing:2007
Number of pages:str. 113-120
Numbering:Tom. 13, vyp. 4
ISSN:1560-5159
UDC:512.643
COBISS_ID:14661977 Link is opened in a new window
Views:1046
Downloads:33
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Secondary language

Language:Slovenian
Abstract:V članku študiramo preslikave, ki transformirajo eno imananto matričnih snopov v drugo. Vnaprej ne predpostavimo niti surjektivnosti, niti linearnosti preslikav. Predpostavimo zgolj šibko linearnost v obliki identitete ▫$d_\chi (\Phi(A) + \lambda \Phi(B)) = d_{\chi'}(A+\lambda B)$▫. Pokažemo, da zgolj ta identiteta implicira avtomatično linearnost in bijektivnost preslikave ▫$\Phi$▫.We study the maps that transform one immanant into another. No surjectivity orlinearity is imposed; the rudiments of the former are weakly embedded into the functional equation via ▫$d_\chi (\Phi(A) + \lambda \Phi(B)) = d_{\chi'}(A+\lambda B)$▫. We show that this property alone implies that ▫$\Phi$▫ is linear and bijective.
Keywords:matematika, linearna algebra, teorija matrik, imanante, ohranjevalci, mathematics, linear algebra, matrix theory, immanants, preservers

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