Continuous Adjacency Preserving Maps on Real Matrices

• Autores: Peter Semrl, Leiba Rodman, Ahmed R. Sourour
• Localización: Canadian mathematical bulletin, ISSN 0008-4395, Vol. 48, Nº 2, 2005, págs. 267-274
• Idioma: inglés
• DOI: 10.4153/cmb-2005-025-6
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• Resumen

  • 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.