All Questions

Suppose that $e_1, \cdots, e_n$ are the standard vectors of the Euclidean space $\mathbb{R}^n$. Let us consider the backward shift operator $T:\mathbb{R}^n\to \mathbb{R}^n$ given by $Te_k=e_{k-1}$ ...

Take a function $f: Z_N\rightarrow R$. Construct an $N \times N$ matrix where the $(i,j)$th element of the matrix is $f(i-j)$, where $i-j$ is interpreted mod $Z_N$. The resulting matrices are ...