PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
Czasopismo
2014 | 2 | 1 |
Tytuł artykułu

Immanant Conversion on Symmetric Matrices

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Letr Σn(C) denote the space of all n χ n symmetric matrices over the complex field C. The main objective of this paper is to prove that the maps Φ : Σn(C) -> Σn (C) satisfying for any fixed irre- ducible characters X, X' -SC the condition dx(A +aB) = dχ·(Φ(Α ) + αΦ(Β)) for all matrices A,В ε Σ„(С) and all scalars a ε C are automatically linear and bijective. As a corollary of the above result we characterize all such maps Φ acting on ΣИ(С).
Słowa kluczowe
Wydawca
Czasopismo
Rocznik
Tom
2
Numer
1
Opis fizyczny
Daty
wydano
2014-01-01
otrzymano
2013-08-29
zaakceptowano
2014-01-03
online
2014-02-12
Twórcy
  • Departamento de Matemática, Faculdade de Ciências, Universidade de Lisboa, Bloco C6, Piso 2, Campo Grande, 1700-016 Lisboa, Portugal, mpcoelho@cii.fc.ul.pt
  • Departamento de Matemática, Faculdade de Ciências, Universidade de Lisboa, Bloco C6, Piso 2, Campo Grande, 1700-016 Lisboa, Portugal, mamonteiro@fc.ul.pt
  • Department of Higher Algebra, Faculty of Mathematics and Mechanics, Moscow State University, Moscow, 119991, Russia, guterman@list.ru
Bibliografia
  • [1] C. Cao, X. Tang: Determinant preserving transformations on symmetric matrix spaces, Electronic Journal of Linear Algebra 11 (2004) 205-211.
  • [2] M. P. Coelho: Linear preservers of the permanent on symmetric matrices, Linear and Multilinear Algebra 41 (1996) 1-8.
  • [3] M. P. Coelho, M. A. Dufner: Immanant preserving and immanant converting maps, Linear Algebra Appl. 418(2006) 177-187.
  • [4] M. P. Coelho, M. A. Dufner: Linear preservers of immanants on symmetric matrices, Linear Algebra Appl. 255 (1997) 314-334.
  • [5] M. P. Coelho, M. A. Dufner: On the conversion of an immanant into another on symmetric matrices, Linear and Multilinear Algebra, 51:2 (2003), 137-145.
  • [6] G. Dolinar and P. Semrl: Determinant preserving maps on matrix algebras, Linear Algebra and its Application 348 (2002) 189-192.
  • [7] G. Frobenius,¨Uber die Darstellung der endlichen Gruppen durch lineare Substitutionen. Sitzungsber. Preuss. Akad. Wiss. Berlin (1897), 994-1015.
  • [8] G.D. James, A. Kerber: The representation theory of the symmetric group, Encyclopedia of Mathematics and its Applications 16, Cambridge University Press, 1981.
  • [9] B. Kuzma: A note on immanant preservers, Fundamental and Applied Mathematics, 13, 4, (2007) 113-120, translated in Journal of Mathematical Sciences (New York) 155:6 (2008), 872-876.
  • [10] M. H. Lim: Linear transformations on symmetric matrices, Linear and Multilinear Algebra 7 (1979) 47-57.
  • [11] D.E. Littlewood: The theory of group characters, Oxford University Press, 1958
  • [12] V. Tan and F. Wang: On determinant preserver problems, Linear Algebra and its Application 369 (2003) 311-317.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_spma-2014-0001
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.