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Linear operators preserving rank equivalence on alternate matrix spaces. (Chinese. English summary) Zbl 1141.15304

Summary: Let \(F\) be any field and \(n\geq 4\) be an integer. Denote by \(K_n(F)\) the space of all \(n\times n\) alternate matrices over \(F\). For \(A, B\in K_n(F)\), 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 \(K_n(F)\). Some applications are also given.

MSC:

15A04 Linear transformations, semilinear transformations
15A03 Vector spaces, linear dependence, rank, lineability
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