Thesis (Ph. D.)--University of Chicago, 1907. / Biographical sketch. "Reprinted from the Transactions of the American mathematical society, v. 11, 1910, p. 449-474." "Presented to the Society (Chicago) March 30, 1907, in somewhat different form under the title: Vector theory, in terms of symbolic differential parameters." Includes bibliographical references.

Thesis (Ph. D.)--University of Chicago, 1907. / Biographical sketch. "Reprinted from the Transactions of the American mathematical society, v. 11, 1910, p. 449-474." "Presented to the Society (Chicago) March 30, 1907, in somewhat different form under the title: Vector theory, in terms of symbolic differential parameters." Includes bibliographical references. Also available on the Internet.

Thesis (Ph. D.)--University of Oregon, 2000. / Typescript. Includes vita and abstract. Includes bibliographical references (leaves 92-93). Also available for download via the World Wide Web; free to University of Oregon users.

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. / Science, Faculty of / Mathematics, Department of / Graduate