Tang, Xiaomin; Chen, Xuemei; Gao, Xiangyu Linear operators preserving rank equivalence on alternate matrix spaces. (Chinese. English summary) Zbl 1141.15304 J. Math. Study 40, No. 1, 80-85 (2007). 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 Keywords:field; rank equivalence; alternate matrix; rank preserving; linear operators PDFBibTeX XMLCite \textit{X. Tang} et al., J. Math. Study 40, No. 1, 80--85 (2007; Zbl 1141.15304)