Rank-deficient submatrices of Kronecker products of Fourier matrices

✍ Scribed by Steven Delvaux; Marc Van Barel

• Publisher: Elsevier Science
• Year: 2007
• Tongue: English
• Weight: 238 KB
• Volume: 426
• Category: Article
• ISSN: 0024-3795
• DOI: 10.1016/j.laa.2007.05.009

✦ Synopsis

We provide a set of maximal rank-deficient submatrices of a Kronecker product of two matrices A ⊗ B, and in particular the Kronecker product of Fourier matrices

We show how in the latter case, maximal rank-deficient submatrices can be constructed as tilings of rank-one blocks. Several such tilings may be associated to any subgroup of the Abelian group Z n 1 × • • • × Z n k that corresponds to the matrix F. The maximal rank-deficient submatrices of F are also related to an uncertainty principle for Fourier transforms over finite Abelian groups, for which we can then obtain stronger versions.