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- W2051584562 abstract "Let K be an arbitrary (commutative) field, and V be a linear subspace of Mn(K) such that codim V<n-1. Using a recent generalization of a theorem of Atkinson and Lloyd [9], we show that every linear embedding of V into Mn(K) which strongly preserves non-singularity must be M↦PMQ or M↦PMTQ for some pair (P,Q) of non-singular matrices of Mn(K), unless n=3, codim V=1 and K≃F2. This generalizes a classical theorem of Dieudonné with a similar strategy of proof. Weak linear preservers are also discussed, as well as the exceptional case of a hyperplane of M3(F2)." @default.
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- W2051584562 date "2012-05-01" @default.
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- W2051584562 title "The linear preservers of non-singularity in a large space of matrices" @default.
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- W2051584562 doi "https://doi.org/10.1016/j.laa.2011.12.027" @default.
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