J. Alaminos (Author), Matej Brešar (Author), J. Extremera (Author), A. R. Villena (Author)

Abstract

Naj bo ▫$M_n$▫, ▫$n \geqslant 2$▫, algebra vseh ▫$n \times n$▫ matrik nad poljem ▫$F$▫ karakteristike različne od 2, in naj bo ▫$\Phi$▫ bilinearna preslikava iz ▫$M_n \times M_n$▫ v poljubni vektorski prostor ▫$X$▫ nad ▫$F$▫. Glavni izrek pove,da je iz pogoja, da je ▫$\phi(e, f ) = 0$▫ za vse ortogonalne idempotente ▫$e$▫ in ▫$f$▫ ranga 1 sledi eksistenca linearnih takih preslikav ▫$\Phi_1,\Phi_2 \colon M_n \to X$▫, da je ▫$\phi(a,b) = \Phi_1(ab) + \Phi_2(ba)$▫ za vse ▫$a,b \in M_n$▫. Izrek se uporabi pri študiju nekaterih problemov o linearnih ohranjevalcih.

Keywords

matematika;teorija matrik;matrična algebra;ničelni produkt;idempotent ranga 1;linearna preslikava;bilinearna preslikava;linearni ohranjevalci;mathematics;matrix theory;matrix algebra;zero product;rank one idempotent;linear map;bilinear map;linear preserver problem;

Data

Language: English
Year of publishing:
Typology: 1.01 - Original Scientific Article
Organization: UM FNM - Faculty of Natural Sciences and Mathematics
UDC: 512.643
COBISS: 15331161 Link will open in a new window
ISSN: 0024-3795
Views: 977
Downloads: 85
Average score: 0 (0 votes)
Metadata: JSON JSON-RDF JSON-LD TURTLE N-TRIPLES XML RDFA MICRODATA DC-XML DC-RDF RDF

Other data

Secondary language: Unknown
Secondary abstract: Let ▫$M_n$▫, ▫$n \geqslant 2$▫, be the algebra of all ▫$n \times n$▫ matrices over afield ▫$F$▫ of characteristic not 2, and let ▫$\Phi$▫ be a bilinear map from ▫$M_n \times M_n$▫ into an arbitrary vector space ▫$X$▫ over ▫$F$▫. Our main result states that if ▫$\phi(e, f ) = 0$▫ whenever ▫$e$▫ and ▫$f$▫ are orthogonal rank one idempotents, then there exist linear maps ▫$\Phi_1,\Phi_2 \colon M_n \to X$▫ such that ▫$\phi(a,b) = \Phi_1(ab) + \Phi_2(ba)$▫ for all ▫$a,b \in M_n$▫. This is applicable to some linear preserver problems.
Secondary keywords: matematika;teorija matrik;matrična algebra;ničelni produkt;idempotent ranga 1;linearna preslikava;bilinearna preslikava;linearni ohranjevalci;
URN: URN:SI:UM:
Type (COBISS): Not categorized
Pages: str. 738-743
Volume: ǂVol. ǂ432
Issue: ǂiss. ǂ2-3
Chronology: 2009
ID: 1474520