Cao Chong-guang
Abstract
Suppose F is a field. Let M_n(F) be the linear space of all n×n matrices over F. Firstly, all linear maps from M_n(F) to M_m(F) preserving inverses of matrices are characterized when chF≠2. Secondly, the nonsingular linear maps from M_n(F) to M_n(F) preserving inverses of matrices are also characterized when ch F=2.
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Suppose F is a field. Let M_n(F) be the linear space of all n×n matrices over F. Firstly, all linear maps from M_n(F) to M_m(F) preserving inverses of matrices are characterized when chF≠2. Secondly, the nonsingular linear maps from M_n(F) to M_n(F) preserving inverses of matrices are also characterized when ch F=2.
Key concepts: Invertible matrix, Mathematics, Inverse, Linear map, Linear space, Combinatorics, Field (mathematics), Space (punctuation)