Generalized matrix functions and determinants

• Autorzy: Mohammad Jafari , Ali Madadi
• Języki publikacji: EN

Abstrakty

EN

In this paper we prove that, up to a scalar multiple, the determinant is the unique generalized matrix function that preserves the product or remains invariant under similarity. Also, we present a new proof for the known result that, up to a scalar multiple, the ordinary characteristic polynomial is the unique generalized characteristic polynomial for which the Cayley-Hamilton theorem remains true.

Słowa kluczowe

EN

Generalized matrix functions; Determinants; Generalized characteristic polynomials

Kategorie tematyczne

• 15A15: Determinants, permanents, other special matrix functions

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2014
• Tom: 12
• Numer: 3
• Strony: 464-469

Daty

wydano

2014-03-01

online

2013-12-21

Twórcy

autor

Mohammad Jafari

• University of Tabriz

autor

Ali Madadi

• University of Tabriz

Bibliografia

• [1] Beasley L.B., Cummings L.J., On the uniqueness of generalized matrix functions, Proc. Amer. Math. Soc., 1983, 87(2), 229–232 http://dx.doi.org/10.1090/S0002-9939-1983-0681826-6[Crossref]
• [2] Darafsheh M.R., Mallahi K., Pournaki M.R., A note on Cayley-Hamilton theorem for generalized matrix function, Pure Math. Appl., 2000, 11(4), 553–557
• [3] Jafari M.H., Madadi A.R., On the equality of generalized matrix functions, Linear Algebra Appl. (in press), DOI: 10.1016/j.laa.2012.04.027 [Crossref]
• [4] Marcus M., Finite Dimensional Multilinear Algebra, I, Pure Appl. Math., 23, Marcel Dekker, New York, 1973
• [5] Merris R., Generalized matrix functions: a research problem, Linear and Multilinear Algebra, 1979/80, 8(1), 83–86 http://dx.doi.org/10.1080/03081087908817302[Crossref]
• [6] Merris R., Multilinear Algebra, Algebra Logic Appl., 8, Gordon and Breach, Amsterdam, 1997
• [7] Zhang F., Matrix Theory, 2nd ed., Universitext, Springer, New York, 2011 http://dx.doi.org/10.1007/978-1-4614-1099-7[Crossref]

Identyfikatory

DOI

10.2478/s11533-013-0347-0