标题： 通过几何不变量的绝对非奇异张量之间的非等价性测试 显示英文标题

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

摘要： 4x4x3 绝对非奇异张量由其行列式多项式表征。 绝对非奇异张量在不改变张量秩的一类线性变换下的非等价性被研究。 理论上表明，行列式多项式的常值曲面的仿射几何不变量有助于区分绝对非奇异张量的非等价性。 还给出了数值计算，并证明这些不变量确实有用。 还对通过20球面设计计算不变量进行了评论。 我们表明，张量数据分析中的代数问题可以通过仿射几何方法来解决。 显示英文摘要

摘要： 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.