Preservers of matrix pairs with bounded distance

Lim, Ming-Huat and Tan , Joshua Juat-Huan (2007) Preservers of matrix pairs with bounded distance. In: The 3 rd IMT-GT 2007 Regional Conference on Mathematics, Statistics and Applications, 5-6 Dec 2007.

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Abstract

Let m, n and k be positive integers such that 2 · k < n · m. Let V denote either the vector space of all m£n matrices over a ¯eld with at least three elements or the vector space of all n £ n Hermitian matrices over a ¯eld F of characteristic 2 associated with an involution. We characterize surjective mappings T from onto itself such that for every pair A;B 2 V , rank(A ¡ B) · k if and only if rank(T(A) ¡ T(B)) · k.

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