On preservers of determinant over a field

• Autorzy: Kalinowski J.
• Języki publikacji: EN

Abstrakty

EN

Operators preserving the determinant of real matrices were studied in [1], [2] and [5] under assumption that the operator is linear. In this paper the linearity of the operators is not assumed: we only assume that the operators are of the form F = [fi,j], where functions fij : [...], we characterize these operators from [...] into itself preserving the determinant. An operator preserving the determinant of matrices must be linear as in [4]. The form of operator F is presented.

Słowa kluczowe

EN

opeartors; determinants; operators preserving determinant

PL

operatory; wyznaczniki; liniowe zagadnienia wyznaczników

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2008
• Tom: Vol. 41, nr 3
• Strony: 519--524
• Opis fizyczny: Bibliogr. 5 poz.

Twórcy

autor

Kalinowski J.

• Department of Mathematics Silesian University Bankowa 14 40-007 Katowice, Poland,

Bibliografia

• [1] G. Dolinar, P. Šemrl, Determinant preserving maps on matrix algebras, Linear Algebra Appl. 348 (2002), 189-192.
• [2] G. Fröbenius, Über die Darstellung der endlichen Gruppen durch lineare substitutionen, Sitzungsberg Deutsch. Akad. Wiss. Berlin (1897), 994-1015.
• [3] J. Kalinowski, On operators preserving the permanents, Intern. J. Pure Appl. Math. 38 (2007), 5-11.
• [4] C. K. Li, S. Pierce, Linear preserver problems, Amer. Math. Monthly 108 (2001), 591-605.
• [5] F. Wang, V. Tan, On determinant preserver problems, Linear Algebra Appl. 369 (2003), 311-317.