Linear maps leaving the alternating group invariant Original Research Article

Let An be the group of n×n even permutation matrices, and let Vn be the real linear space spanned by An. The purpose of this note is to characterize those linear operators φ on Vn satisfying φ(An)=An. This answers a question raised by C.K. Li, B.S. Tam, N.K. Tsing [Linear Algebra Appl., to appear].