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Linear/additive preservers of rank 2 on spaces of alternate matrices over fields. (English) Zbl 1075.15009
A matrix AM n (F) is said to be alternate if x t Ax=0 for every xM n,1 (F). If the characteristic of F is not 2, A is alternate iff A is skew-symmetric, and if char(F)=2, A is alternate iff it is symmetric. The author obtains a characterization of additive transformations on the space of alternate matrices which preserve the set of rank-2 matrices on the fields which are not isomorphic to their proper subfields. The characterization of the corresponding linear transformations is given for an arbitrary field.
15A04Linear transformations, semilinear transformations (linear algebra)
15A03Vector spaces, linear dependence, rank
15A33Matrices over special rings