E-Characteristic Polynomials of Tensors
E-Characteristic Polynomials of Tensors
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DOI：
10.4310/cms.2013.v11.n1.a2
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发表时间：
2012-08
期刊：
影响因子：
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通讯作者：
An-Min Li;L. Qi;Bin Zhang
中科院分区：
文献类型：
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作者：
An-Min Li;L. Qi;Bin Zhang
本文证明了张量的E-特征多项式的系数是该张量的正交不变量。当维数为2时，给出了E-特征多项式的简化公式。给出了E-特征多项式常数项的计算公式。然后，我们研究了具有无穷多个特征对的张量集合和非正则张量集合，证明了这两个集合作为张量射影空间中的子簇具有余维数2。这使得我们的微扰方法可行。利用微扰方法，通过探讨E-特征值与特征对等价类之间的区别，给出了E-特征多项式首项系数的一个简单公式，当维数为2时.
In this paper, we show that the coefficients of the E-characteristic polynomial of a tensor are orthonormal invariants of that tensor. When the dimension is 2, some simplified formulas of the E-characteristic polynomial are presented. A re- sultant formula for the constant term of the E-characteristic polynomial is given. We then study the set of tensors with infinitely many eigenpairs and the set of irregular tensors, and prove both the sets have codimension 2 as subvarieties in the projective space of tensors. This makes our perturbation method workable. By using the perturbation method and exploring the difference between E-eigenvalues and eigenpair equivalence classes, we present a simple formula for the coefficient of the leading term of the E-characteristic polynomial, when the dimension is 2.