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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.
MSC:
15A04Linear transformations, semilinear transformations (linear algebra)
15A03Vector spaces, linear dependence, rank
15A33Matrices over special rings