The singular linear preservers of non-singular matrices
Rings and Algebras
2010-05-06 v2
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 Dieudonn\'e's theorem on singular subspaces of M_n(K), also yields a proof for the classical non-singular case.
Cite
@article{arxiv.1002.1732,
title = {The singular linear preservers of non-singular matrices},
author = {Clément de Seguins Pazzis},
journal= {arXiv preprint arXiv:1002.1732},
year = {2010}
}
Comments
12 pages, some minor corrections from the first version