对称矩阵空间上保对合的映射(英文)

Maps on spaces of symmetric matrices preserving involution relation

设F是一个元素个数大于2的域, S2(F)是F上的2×2对称矩阵空间。对任意的A,B∈S2(F)和λ∈F,如果A-λB是对合当且仅当Φ(A)-λΦ(B)是对合,则称映射Φ:S2(F)→S2(F)是保对合关系的。当F的特征不为2时刻画了Φ的形式。

Suppose F is an arbitrary field with at least three elements. Let S2 （F） be the space of all 2 × 2 symmetric matrices over F. A map Φ：S2（F）→S2（F） is said to preserve involution relation if A - λB is an involution if and only if Φ（A）-λΦ（B） is an involution for any A,B ∈S2 （F） and λ ∈ F. When the characteristic of F is not 2, the structure of Ф is described.