Continuous Adjacency Preserving Maps on Real Matrices 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. Keywords:adjacency of matrices, continuous preservers, affine transformationsCategories:15A03, 15A04.