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Which topic(s) does this matrix come from? What is the name of this matrix?


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That's a Vandermonde matrix, as well as the matrix of the discrete Fourier transform of size $3$... It is not quite clear what the purpose of this question is, though! – Mariano Suárez-Alvarez Feb 10 '12 at 5:28
We are assuming that $\omega$ here is a root of unity, of course (too bad OP did not define his/her notation)... if not, then it's just some symmetric matrix. – J. M. Feb 10 '12 at 5:44

This is the discrete Fourier transform matrix of size $3$. It naturally appears mathematically in the representation theory (don't be intimidated by this!) of the cyclic groups $\mathbb{Z}/n\mathbb{Z}$, as well as practically in signal processing and related fields.

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