Cyclic operators for columns of the matrices of discrete transforms
type: Item
instance of: scholarly article
title: Cyclic operators for columns of the matrices of discrete transforms
zbMATH Open document ID: 1329.65329
author: M. S. Bespalov
published in: Journal of Mathematical Sciences (New York)
publication date: 2015-10-23T00:00:00Z
review text: The author considers cyclic permutations of the columns of a matrix and their application to Hadamard-Sylvester matrices of order \(2^n\). Investigated are recursive algorithms for the construction of such permutations of discrete Walsh transforms in both the Hadamard and the Paley enumerations, along with results on eigenspaces and connection to the Fourier transform of the auxiliary matrices appearing in these algorithms. For the background of this work, see, e.g., the author's paper [Probl. Inf. Transm. 46, No. 3, 253--271 (2010); translation from Probl. Peredachi Inf. 46, No. 3, 60--79 (2010; Zbl 1241.94018)] and the book by Schipp, Wade, and Simon [\textit{F. Schipp} et al., Walsh series. An introduction to dyadic harmonic analysis. With the assistance from J. Pál. Bristol etc.: Adam Hilger (1990; Zbl 0727.42017)].
reviewed by: Gisbert Stoyan
Mathematics Subject Classification ID: 65T50
Mathematics Subject Classification ID: 65F30
Mathematics Subject Classification ID: 42C10
Mathematics Subject Classification ID: 15A04
Mathematics Subject Classification ID: 15B34
zbMATH DE Number: 6497499
zbMATH Keywords: cyclic operators
zbMATH Keywords: discrete Walsh transform
zbMATH Keywords: Hadamard-Sylvester matrix
zbMATH Keywords: recursive algorithm
zbMATH Keywords: Hadamard enumeration
zbMATH Keywords: Paley enumeration
zbMATH Keywords: Fourier transform
MaRDI profile type: Publication
full work available at URL: s10958-015-2421-6
OpenAlex ID: W845885948
cites work: Q5331504
cites work: Q4217269
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cites work: Eigenspaces of the discrete Walsh transform
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cites work: Q3997391
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cites work: On the properties of a new tensor product of matrices
DOI: 10.1007/S10958-015-2421-6
description: scientific article; zbMATH DE number 6497499