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Linear transformations of symmetric tensor spaces which preserve rank 1 Cummings, Larry
Abstract
If r > 1 is an integer then U(r) denotes the vector space of r-fold symmetric tensors and Pr[U] is the set of rank 1 tensors in U(r). Let U be a finite-dimensional vector space over an algebraically closed field of characteristic not a prime p if r = p[formula omitted] for some positive integer k. We first determine the maximal subspaces of rank 1 symmetric tensors. Suppose h is a linear mapping of U(r) such that h(Pr[U]) ⊆ Pr[U] and ker h ⋂ Pr[U] = 0. We have shown that every such h is induced by a non-singular linear mapping of U, provided dim U > r+1 . This work partially answers a question raised by Marcus and Newman (Ann. of Math., 75, (1962) p.62.).
Item Metadata
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Linear transformations of symmetric tensor spaces which preserve rank 1
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Creator | |
Publisher |
University of British Columbia
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Date Issued |
1967
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Description |
If r > 1 is an integer then U(r) denotes the vector space of r-fold symmetric tensors and Pr[U] is the set of rank 1 tensors in U(r). Let U be a finite-dimensional vector space over an algebraically closed field of characteristic not a prime p if r = p[formula omitted] for some positive integer k. We first determine the maximal subspaces of rank 1 symmetric tensors. Suppose h is a linear mapping of U(r) such that h(Pr[U]) ⊆ Pr[U] and ker h ⋂ Pr[U] = 0. We have shown that every such h is induced by a non-singular linear mapping of U, provided dim U > r+1 . This work partially answers a question raised by Marcus and Newman (Ann. of Math., 75, (1962) p.62.).
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Language |
eng
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Date Available |
2011-08-26
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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 |
10.14288/1.0080592
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Degree Grantor |
University of British Columbia
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Scholarly Level |
Graduate
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DSpace
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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.