Decomposable tensors as a quadratic variety
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- by Robert Grone PDF
- Proc. Amer. Math. Soc. 64 (1977), 227-230 Request permission
Abstract:
Let ${V_i}$ be a finite dimensional vector space over a field F for each $i = 1,2, \ldots ,m$, and let z be a tensor in ${V_1} \otimes \cdots \otimes {V_m}$. In this paper a set of homogeneous quadratic polynomials in the coordinates of z is exhibited for which the associated variety is the set of decomposable tensors. In addition, a question concerning the maximal tensor rank in such a situation is answered, and an application to other symmetry classes of tensors is cited.References
- Marvin Marcus, Finite dimensional multilinear algebra. Part II, Pure and Applied Mathematics, Vol. 23, Marcel Dekker, Inc., New York, 1975. MR 0401796
- Marvin Marcus, A dimension inequality for multilinear functions, Inequalities, III (Proc. Third Sympos., Univ. California, Los Angeles, Calif., 1969; dedicated to the memory of Theodore S. Motzkin), Academic Press, New York, 1972, pp. 217–224. MR 0332849
- William Watkins, Linear maps and tensor rank, J. Algebra 38 (1976), no. 1, 75–84. MR 424855, DOI 10.1016/0021-8693(76)90244-1
Additional Information
- © Copyright 1977 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 64 (1977), 227-230
- MSC: Primary 14M15; Secondary 15A69
- DOI: https://doi.org/10.1090/S0002-9939-1977-0472853-X
- MathSciNet review: 0472853