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UBC Theses and Dissertations
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.
Item Metadata
Title |
Characterization of subspaces of rank two grassmann vectors of order two
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Creator | |
Publisher |
University of British Columbia
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Date Issued |
1967
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Description |
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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Genre | |
Type | |
Language |
eng
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Date Available |
2012-03-07
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Provider |
Vancouver : University of British Columbia Library
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Rights |
For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use.
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DOI |
10.14288/1.0080623
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URI | |
Degree | |
Program | |
Affiliation | |
Degree Grantor |
University of British Columbia
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Campus | |
Scholarly Level |
Graduate
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Aggregated Source Repository |
DSpace
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Item Media
Item Citations and Data
Rights
For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use.