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Adjacency preserving mappings on real symmetric matrices

Peter Legiša ; Department of Mathematics, FMF, University of Ljubljana, Ljubljana, Slovenia


Puni tekst: engleski pdf 238 Kb

str. 419-432

preuzimanja: 794

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Sažetak

Let Sn denote the space of all n×n real symmetric matrices.
Let n2 and let Φ:Sn\raSm be a map
preserving adjacency, i.e. if A,BSn and rank (AB)=1,
then rank (Φ(A)Φ(B))=1. If Φ(0)=0,
we prove that either:
(i) Φ maps Sn into \rrB, where B is a rank one matrix, or (ii) there exist c{1,1} and RMm invertible (mn) such that for ASn,
Φ(A)=cR[A000]RT.
(If m=n, the zeros on the right-hand side are absent.)

Ključne riječi

real symmetric matrix; adjacency preserving map; rank; geometry of matrices

Hrčak ID:

74883

URI

https://hrcak.srce.hr/74883

Datum izdavanja:

21.12.2011.

Posjeta: 1.480 *

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