Factoring Matrices into the Product of Circulant and Diagonal Matrices

Marko Huhtanen*, Allan Perämäki

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

7 Citations (Scopus)

Abstract

A generic matrix $$A\in \,\mathbb {C}^{n \times n}$$A∈Cn×n is shown to be the product of circulant and diagonal matrices with the number of factors being $$2n-1$$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.

Original languageEnglish
Pages (from-to)1018-1033
Number of pages16
JournalJournal of Fourier Analysis and Applications
Volume21
Issue number5
DOIs
Publication statusPublished - 26 Mar 2015
MoE publication typeA1 Journal article-refereed

Keywords

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

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