Some Remarks on the Plücker Relations
نویسندگان
چکیده
Proof. (1) These are the well known classical Plücker relations. For completeness’ sake we include a proof. Let P ∈ ΛV and consider the induced linear mapping ♯P : Λ V ∗ → V . Its image, W , is contained in each linear subspace U of V with P ∈ ΛU . Thus W is the minimal subspace with this property. P is decomposable if and only if dimW = s, and this is the case if and only if w ∧ P = 0 for each w ∈ W . But iΦP for φ ∈ Λ V ∗ is the typical element in W .
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