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.). / Science, Faculty of / Mathematics, Department of / Graduate
| Identifer | oai:union.ndltd.org:UBC/oai:circle.library.ubc.ca:2429/36934 |
| Date | January 1967 |
| Creators | Cummings, Larry |
| Publisher | University of British Columbia |
| Source Sets | University of British Columbia |
| Language | English |
| Detected Language | English |
| Type | Text, Thesis/Dissertation |
| 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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