| Home > Publications > Reports > Numerical Analysis and Applied Mathematics (TW) |
TW 477
Steven Delvaux, Marc Van Barel
Rank-deficient submatrices of Kronecker products of Fourier matrices
Abstract
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 F=Fn1⊗...⊗ Fnk. We show how in the latter case, maximal rank-deficient submatrices can be constructedas tilings of rank-one blocks. Such tilings exist for any subgroup of a suitable Abelian group associated to the matrix F. These maximal rank-deficient submatrices are also related to an uncertainty principle for Fourier transforms over finite Abelian groups, for which we can then obtain stronger versions.
report.pdf (375K) / mailto: M. Van Barel