2006•Journal of Science of Teachers' College and UniversityRequires access

Linear maps preserving inverses of upper triangular matrices over fields

Haiyan Wu

Abstract

Suppose F is a field with the number of elements larger than 3,n2 is a positive integer.Let(M_n(F)) and T_n(F) be the linear spaces of n×n full matrices and upper triangular matrices over F,respectively.The paper first characterizes all linear injective maps from T_n(F) to M_n(F) preserving inverses of matrices,and thereby all linear bijective maps from T_n(F) to itself preserving inverses of matrices are characterized.

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Key concepts: Injective function, Mathematics, Triangular matrix, Bijection, Integer (computer science), Combinatorics, Linear map, Field (mathematics)