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Characterization of subspaces of rank two grassmann vectors of order two Lim, Marion Josephine Sui Sim

Abstract

Let U be an n-dimensional vector space over an algebraically closed field. Let [formula omitted] denote the [formula omitted] space spanned by all Grassmann products [formula omitted]. Subsets of vectors of [formula omitted] denoted by [formula omitted] and [formula omitted] are defined as follows [formula omitted]. A vector which is in [formula omitted] or is zero is called pure or decomposable. Each vector in [formula omitted] is said to have rank one. Similarly each vector in [formula omitted] has rank two. A subspace of H of [formula omitted] is called a rank two subspace If [formula omitted] is contained in [formula omitted]. In this thesis we are concerned with investigating rank two subspaces. The main results are as follows: If dim [formula omitted] such that every nonzero vector [formula omitted] is independent in U. The rank two subspaces of dimension less than four are also characterized.

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