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Let $N$ be a natural number and let $w$ be a complex number. We define the $N\times N$ matrix $C_w=(a_{k,l})_{k,l=1}^N$ as follows, $$ a_{k,l}=\begin{cases}1 & l=k+1\\ w &...

Discrete Fourier transform (DFT) has only four distinct eigenvalues: $±1$ and $±i$. For large matrices , each eigenvalue $λ$ yields a multidimensional eigenspace, allowing linear combinations of ...

I have the $N$x$N$ matrix below where $N$ is a power of 2 (usually 64 or 256) and $\omega = 2\pi/N$. What is its largest eigenvalue? $\begin{bmatrix} 2 & 1 & 0 & 0 & \cdots & 0 &...