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

Toshio Sakata; Kazumitsu Maehra; Takeshi Sasaki; Toshio Sumi; Mitsuhiro Miyazaki; Yoshitaka Watanabe

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arXiv · 1009.2723

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

Toshio Sakata·Kazumitsu Maehra·Takeshi Sasaki·Toshio Sumi·Mitsuhiro Miyazaki·Yoshitaka Watanabe

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Abstract

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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Toshio Sakata, Kazumitsu Maehra, Takeshi Sasaki, Toshio Sumi, Mitsuhiro Miyazaki, Yoshitaka Watanabe. 2010-09-14. Tests of Non-Equivalence among Absolutely Nonsingular Tensors through Geometric Invariants. https://arxiv.org/abs/1009.2723

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