Nondegeneracy of eigenvectors and singular vector tuples of tensors

نویسندگان

چکیده

In this article, nondegeneracy of singular vector tuples, Z-eigenvectors and eigenvectors tensors is studied, which have found many applications in diverse areas. The main results are: (i) each (Z-)eigenvector/singular tuple a generic tensor nondegenerate, (ii) nonzero Z-eigenvector/singular an orthogonally decomposable nondegenerate.

برای دانلود باید عضویت طلایی داشته باشید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

The Number of Singular Vector Tuples and Uniqueness of Best Rank-One Approximation of Tensors

In this paper we discuss the notion of singular vector tuples of a complex valued d-mode tensor of dimension m1 × . . . × md. We show that a generic tensor has a finite number of singular vector tuples, viewed as points in the corresponding Segre product. We give the formula for the number of singular vector tuples. We show similar results for tensors with partial symmetry. We give analogous re...

متن کامل

The E-Eigenvectors of Tensors

We first show that the eigenvector of a tensor is well-defined. The differences between the eigenvectors of a tensor and its E-eigenvectors are the eigenvectors on the nonsingular projective variety S = {x ∈ P | n

متن کامل

Group Comparison of Eigenvalues and Eigenvectors of Diffusion Tensors

Diffusion tensor imaging (DTI) data differ from most medical images in that values at each voxel are not scalars, but 3×3 symmetric positive definite matrices called diffusion tensors (DTs). The anatomic characteristics of the tissue at each voxel are reflected by the DT eigenvalues and eigenvectors. In this article we consider the problem of testing whether the means of two groups of DT images...

متن کامل

The Asymptotic Number of Simple Singular Vector Tuples of a Cubical Tensor

S. Ekhad and D. Zeilberger recently proved that the multivariate generating function for the number of simple singular vector tuples of a generic m1 × · · · ×md tensor has an elegant rational form involving elementary symmetric functions, and provided a partial conjecture for the asymptotic behavior of the cubical case m1 = · · · = md. We prove this conjecture and further identify completely th...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

ژورنال

عنوان ژورنال: Science China-mathematics

سال: 2022

ISSN: ['1674-7283', '1869-1862']

DOI: https://doi.org/10.1007/s11425-020-1863-5