Abstract
AbstractIt 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 ⟼ 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.
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