Continuous Adjacency Preserving Maps on Real Matrices

[摘要] It is proved that every adjacency preserving continuous map on the vector space of real matrices of fixed size, is either abijective affine tranformation of the form $ A mapsto PAQ+R$, possibly followed by the transposition ifthe matrices are of square size, or its range is contained in a linear subspace consisting of matrices of rank at most onetranslated by some matrix $R$. The result extends previously known theorems where the map was assumed to be also injective.

[学科分类] 数学（综合）

[关键词] adjacency of matrices;continuous preservers;affine transformations