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Journal of Fourier Analysis and Applications

, Volume 21, Issue 5, pp 1018–1033 | Cite as

Factoring Matrices into the Product of Circulant and Diagonal Matrices

  • Marko Huhtanen
  • Allan Perämäki
Article

Abstract

A generic matrix \(A\in \,\mathbb {C}^{n \times n}\) is shown to be the product of circulant and diagonal matrices with the number of factors being \(2n-1\) at most. The demonstration is constructive, relying on first factoring matrix subspaces equivalent to polynomials in a permutation matrix over diagonal matrices into linear factors. For the linear factors, the sum of two scaled permutations is factored into the product of a circulant matrix and two diagonal matrices. Extending the monomial group, both low degree and sparse polynomials in a permutation matrix over diagonal matrices, together with their permutation equivalences, constitute a fundamental sparse matrix structure. Matrix analysis gets largely done polynomially, in terms of permutations only.

Keywords

Circulant matrix Diagonal matrix Sparsity structure  Matrix factoring Polynomial factoring Multiplicative Fourier compression 

Mathematics Subject Classification

15A23 65T50 65F50 12D05 

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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Department of Mathematical SciencesUniversity of OuluOulu 57Finland
  2. 2.Department of Mathematics and Systems AnalysisAalto UniversityEspooFinland

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