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Rank-deficient submatrices of Fourier matrices. (English) Zbl 1149.42005

Summary: We consider the maximal rank-deficient submatrices of Fourier matrices with order a power of a prime number. We do this by considering a hierarchical subdivision of these matrices into low rank blocks. We also explore some connections with the fast Fourier transform (FFT), and with an uncertainty principle for Fourier transforms over finite abelian groups.

MSC:

42A99 Harmonic analysis in one variable
15A03 Vector spaces, linear dependence, rank, lineability
15A23 Factorization of matrices
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