On 2D Inverse Problems/Fourier coordinates

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Let Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "/mathoid/local/v1/":): \omega 
 be a not unit N'th root of unity, i.e. .

The discrete Fourier transform 's given by the symmetric Vandermonde matrix:
For example,
Exercise (*). The square of the Fourier transform is the identity transform:
Exercise (*). If an e-network is rotation invariant, then so 's the conductivity equation and the Dirichlet-to-Neumann map is diagonal in the Fourier coordinates (the column vectors of the matrix.