Continuous Adjacency Preserving Maps on Real Matrices
Canadian mathematical bulletin, Tome 48 (2005) no. 2, pp. 267-274
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It is proved that every adjacency preserving continuous map on the vector space of real matrices of fixed size, is either a bijective affine tranformation of the form $A\,\mapsto \,PAQ\,+\,R$ , possibly followed by the transposition if the matrices are of square size, or its range is contained in a linear subspace consisting of matrices of rank at most one translated by some matrix $R$ . The result extends previously known theorems where the map was assumed to be also injective.
Mots-clés :
15A03, 15A04, adjacency of matrices, continuous preservers, affine transformations
Rodman, Leiba; Šemrl, Peter; Sourour, Ahmed R. Continuous Adjacency Preserving Maps on Real Matrices. Canadian mathematical bulletin, Tome 48 (2005) no. 2, pp. 267-274. doi: 10.4153/CMB-2005-025-6
@article{10_4153_CMB_2005_025_6,
author = {Rodman, Leiba and \v{S}emrl, Peter and Sourour, Ahmed R.},
title = {Continuous {Adjacency} {Preserving} {Maps} on {Real} {Matrices}},
journal = {Canadian mathematical bulletin},
pages = {267--274},
year = {2005},
volume = {48},
number = {2},
doi = {10.4153/CMB-2005-025-6},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2005-025-6/}
}
TY - JOUR AU - Rodman, Leiba AU - Šemrl, Peter AU - Sourour, Ahmed R. TI - Continuous Adjacency Preserving Maps on Real Matrices JO - Canadian mathematical bulletin PY - 2005 SP - 267 EP - 274 VL - 48 IS - 2 UR - http://geodesic.mathdoc.fr/articles/10.4153/CMB-2005-025-6/ DO - 10.4153/CMB-2005-025-6 ID - 10_4153_CMB_2005_025_6 ER -
%0 Journal Article %A Rodman, Leiba %A Šemrl, Peter %A Sourour, Ahmed R. %T Continuous Adjacency Preserving Maps on Real Matrices %J Canadian mathematical bulletin %D 2005 %P 267-274 %V 48 %N 2 %U http://geodesic.mathdoc.fr/articles/10.4153/CMB-2005-025-6/ %R 10.4153/CMB-2005-025-6 %F 10_4153_CMB_2005_025_6
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