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Given a quadratic extension L/K of fields and a regular λ-Hermitian space (V, h) of finite dimension over L, we study the orbits of the group of isometries of (V, h) in the set of hyperbolic K-substructures of V.
We give a short overview on the subject of canonical reduction of a pair of bilinear forms, each being symmetric or alternating, making use of the classification of pairs of linear mappings between vector spaces given by J. Dieudonné.
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