paper

The singular linear preservers of non-singular matrices

arXiv:1002.1732 · doi:10.1016/j.laa.2010.03.021

Abstract

Given an arbitrary field K, we reduce the determination of the singular endomorphisms 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 Dieudonné's theorem on singular subspaces of M_n(K), also yields a proof for the classical non-singular case.

12 pages, some minor corrections from the first version

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