Generated Algorithms

Notation

$ \operatorname{diag}(x_1,\dots,x_n)$ diagonal matrix with entries $ x_i$
$ [\sigma, n]$ $ [\delta_{i^\sigma j}\mid i,j\in\{1,\dots,n\}]$, $ (n\times n)$-permutation matrix for permutation $ \sigma$, which is given in cycle notation
$ [\sigma, (x_1,\dots,x_n)$ $ [\sigma, n]\cdot \operatorname{diag}(x_1,\dots,x_n)$ monomial $ (n\times n)$-matrix
$ \omega_n$ primitive $ n$th root of unity, e.g. $ e^{2\pi i/n}$
$ {\mathbf{1}}_n$ identity matrix of degree $ n$
$ \operatorname{R}_\alpha$ rotation matrix $ \genfrac{[}{]}{0pt}{0}{\phantom{-}\cos(\alpha)\,\sin(\alpha)}{-\sin(\alpha)\,\cos(\alpha)}$
$ \operatorname{DFT}_n$ discrete Fourier transform $ [\omega_n^{k\ell}\mid k,\ell = 0\dots n-1]$
$ A\oplus B$ direct sum of $ A$ and $ B$: $ \genfrac{[}{]}{0pt}{0}{A\ 0}{\,0\ B}$
$ A\otimes B$ tensor or Kronecker product of $ A$ and $ B$