交错阵空间上保秩等价的线性算子

Linear Operators Preserving Rank Equivalence on Alternate Matrix Spaces

设F是任意域,n≥4是一个正整数.令Kn(F)是F上n×n交错阵空间.对于A,B∈Kn(F),如果rank A=rank B,则称A和B是秩等价的.本文主要刻画Kn(F)上的保秩等价的线性算子,并给出一些应用.

Let F be any field and n≥4 be an integer. Denote by Kn（F） the space of all n×n alternate matrices over F. For A, B∈Kn（F）, we say that A and B are rank equivalence if rank A=rank B. In this paper, we characterize the linear operators preserving rank equivalence on Kn（F）. Some applications are also given.