%0 Journal Article
%T The singular linear preservers of non-singular matrices
%A Cl¨Śment de Seguins Pazzis
%J Mathematics
%D 2010
%I arXiv
%R 10.1016/j.laa.2010.03.021
%X Given an arbitrary field K, we reduce the determination of the singular endomorphisms $f$ of M_n(K) that stabilize GL_n(K) to the classification of n-dimensional division algebras over K. Our method, which is based upon Dieudonn\'e's theorem on singular subspaces of M_n(K), also yields a proof for the classical non-singular case.
%U http://arxiv.org/abs/1002.1732v2