The componentwise conditioning of the DFT

Mixed and componentwise condition numbers are useful in order to understand stability properties of algorithms for solving structured linear systems. The DFT (discrete Fourier transform) is an essential building block of these algoritms. We obtain precise estimates of mixed and componentwise condition numbers of the DFT. To this end we explicitly compute certain unimodular vectors (a complex vector is said unimodular if the modulus of all its entries is equal to one) whose DFT is again unimodular.