The linear preservers of non-singularity in a large space of matrices

Details The linear preservers of non-singularity in a large space of matrices The linear preservers of non-singularity in a large space of matrices

2010-04-14

arxiv.org/abs/1004.2467v4

Mathematics

Rings and Algebras

35 pages (v4: added some additional explanations)

Scientific paper

Let K be an arbitrary (commutative) field, and V be a linear subspace of M_n(K) such that codim VPMQ or M->PM^TQ for some pair (P,Q) of non-singular matrices of M_n(K), unless n=3, codim V=1 and K is isomorphic to F_2. This generalizes a classical theorem of Dieudonn\'e with a similar strategy of proof. Weak linear preservers are also discussed, as well as the exceptional case of a hyperplane of M_3(F_2).

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