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)
Pages (from-to)	2934-2947
Number of pages	14
Journal	Linear and Multilinear Algebra
Volume	70
Issue number	15
DOIs	https://doi.org/10.1080/03081087.2020.1819947
State	Published - 2022

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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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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Discrete Fourier transform tensors and their eigenvalues

Abstract

Keywords

ASJC Scopus subject areas

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