Exercise 4.2.5

Answers

We have $F_{4} = [\begin{matrix} 1 & 1 & 1 & 1 \\ 1 & i & - 1 & - i \\ 1 & - 1 & 1 & - 1 \\ 1 & - i & - 1 & i \end{matrix}]$

The eigenvalues of $C$ are $F_{4} c = [\begin{matrix} 1 \\ 0 \\ 0 \\ 0 \end{matrix}]$

The three roots for $1 + z + z^{2} + z^{3} = 0$ are $z = e^{2 πki ∕ 4}$ , for $k = 1, 2, 3$

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2020-03-20 00:00