Universal Journal of Mathematics and Mathematical Sciences
Volume 1, Issue 1, Pages 1 - 28
(January 2012)
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TESTS OF INEQUIVALENCE AMONG ABSOLUTELY NONSINGULAR TENSORS THROUGH GEOMETRIC INVARIANTS
Toshio Sakata, Kazumitsu Maehara, Takeshi Sasaki, Toshio Sumi, Mitsuhiro Miyazaki, Yoshitaka Watanabe and Makoto Tagami
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Abstract: The absolutely nonsingular tensor is characterized by its determinant polynomial. Equivalence among absolutely nonsingular tensors with respect to a class of linear transformations, which do not change the tensor rank, is studied. For absolutely nonsingular tensors, it is shown theoretically that certain affine geometric invariants of the constant hypersurface of a determinant polynomial are useful to detect inequivalence among absolutely nonsingular tensors. Also, numerical calculations are presented and these invariants are shown to be useful indeed for absolutely singular tensors. The calculation of invariants by the use of t-spherical design is also introduced. |
Keywords and phrases: n ´ n ´ p
tensors, determinant polynomials, constant hypersurface, affine
differential geometric invariants, test of inequivalence, t-design. |
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