Equivalence classes of the 3 rd Grassman space over a 5 -dimensional vector space

An equivalence relation is defined on Λ r V , the r t h Grassman space over V and the problem of the determnation of the equivalence classes defined by this relation is considered. For any r and V , the decomposable elements form an equivalence class. For r = 2 , the length of the element determines the equivalence class that it is in. Elements of the same length are equivalent, those of unequal lengths are inequivalent. When r ≥ 3 , the length is no longer a sufficient indicator, except when the length is one. Besides these general questions, the equivalence classes of Λ 3 V , when dim V = 5 are determined.