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Discrete Fourier transform tensors and their eigenvalues
Linear and Multilinear Algebra ( IF 0.9 ) Pub Date : 2020-09-21 , DOI: 10.1080/03081087.2020.1819947 Steven P. Diaz 1 , Adam Lutoborski 1
中文翻译:
离散傅里叶变换张量及其特征值
更新日期:2020-09-21
Linear and Multilinear Algebra ( IF 0.9 ) Pub Date : 2020-09-21 , DOI: 10.1080/03081087.2020.1819947 Steven P. Diaz 1 , Adam Lutoborski 1
Affiliation
ABSTRACT
We study the eigenvalue problem for the discrete Fourier transform (DFT) and the recently introduced collapsed DFT (CDFT). For the CDFT we in certain cases compute its symmetric rank, show it is not orthogonally decomposable, and compute its eigenvalues and eigenvectors. We generalize the theory of eigenvalues and eigenvectors for symmetric tensors to tensor products of symmetric tensors and apply this to the DFT.
中文翻译:
离散傅里叶变换张量及其特征值
摘要
我们研究了离散傅里叶变换 (DFT) 和最近引入的折叠 DFT (CDFT) 的特征值问题。对于 CDFT,我们在某些情况下计算它的对称秩,证明它不是正交可分解的,并计算它的特征值和特征向量。我们将对称张量的特征值和特征向量理论推广到对称张量的张量积,并将其应用于 DFT。