Tests of Non-Equivalence among Absolutely Nonsingular Tensors through Geometric Invariants

Details Tests of Non-Equivalence among Absolutely Nonsingular Tensors through Geometric Invariants Tests of Non-Equivalence among Absolutely Nonsingular Tensors through Geometric Invariants

2010-09-14

arxiv.org/abs/1009.2723v1

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24 pages, 3 figures, 5 tables

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4x4x3 absolutely nonsingular tensors are characterized by their determinant polynomial. Non-quivalence among absolutely nonsingular tensors with respect to a class of linear transformations, which do not chage the tensor rank,is studied. It is shown theoretically that affine geometric invariants of the constant surface of a determinant polynomial is useful to discriminate non-equivalence among absolutely nonsingular tensors. Also numerical caluculations are presented and these invariants are shown to be useful indeed. For the caluculation of invarinats by 20-spherical design is also commented. We showed that an algebraic problem in tensor data analysis can be attacked by an affine geometric method.

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