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Rank-deficient submatrices of Kronecker products of Fourier matrices. (English) Zbl 1124.42008
Summary: We provide a set of maximal rank-deficient submatrices of a Kronecker product of two matrices AB, and in particular the Kronecker product of Fourier matrices F=F n 1 F n k . 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 n 1 ×× 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.
42A99Fourier analysis in one variable
15A03Vector spaces, linear dependence, rank
15A69Multilinear algebra, tensor products