Discrete Fourier transform tensors and their eigenvalues

Steven P. Diaz; Adam Lutoborski

doi:10.1080/03081087.2020.1819947

Discrete Fourier transform tensors and their eigenvalues

Steven P. Diaz, Adam Lutoborski

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

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.

Original language	English (US)
Journal	Linear and Multilinear Algebra
DOIs	https://doi.org/10.1080/03081087.2020.1819947
State	Accepted/In press - 2020

Keywords

15A69
42A38
47A75
Tensors
discrete Fourier transforms
tensor eigenvalues

ASJC Scopus subject areas

Algebra and Number Theory

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10.1080/03081087.2020.1819947

Cite this

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title = "Discrete Fourier transform tensors and their eigenvalues",

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.",

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AB - 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.

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KW - 47A75

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KW - tensor eigenvalues

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Discrete Fourier transform tensors and their eigenvalues

Abstract

Keywords

ASJC Scopus subject areas

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