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Exercise 3.3.3

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$AT = [\begin{matrix} 0 & 0 & 0 & 0 & \dots & 0 \\ t_{0} & t_{- 1} & 0 & 0 & \dots & 0 \\ t_{1} & t_{0} & t_{- 1} & 0 & \dots & 0 \\ 0 & t_{1} & t_{0} & t_{- 1} & 0 & \dots \\ 0 & 0 & \dots & \dots & \dots & \dots \\ 0 & 0 & \dots & t_{1} & t_{0} & t_{- 1} \end{matrix}]$

$T A^{T} = [\begin{matrix} 0 & t_{0} & t_{- 1} & 0 & \dots & 0 \\ 0 & t_{1} & t_{0} & t_{- 1} & \dots & 0 \\ 0 & 0 & t_{1} & t_{0} & t_{- 1} & \dots \\ 0 & 0 & \dots & \dots & \dots & \dots \\ 0 & 0 & 0 & \dots & t_{1} & t_{0} \\ 0 & 0 & \dots & 0 & 0 & t_{1} \end{matrix}]$

So we have $C = AT - T A^{T} = [\begin{matrix} 0 & - t_{0} & - t_{- 1} & 0 & \dots & 0 \\ t_{0} & t_{- 1} - t_{1} & - t_{0} & - t_{- 1} & \dots & 0 \\ t_{1} & t_{0} & t_{- 1} - t_{1} & - t_{0} & - t_{- 1} & \dots \\ 0 & 0 & \dots & \dots & \dots & \dots \\ 0 & 0 & 0 & \dots & t_{- 1} - t_{1} & - t_{0} \\ 0 & 0 & \dots & t_{1} & t_{0} & t_{- 1} - t_{1} \end{matrix}]$

niuers

2020-03-20 00:00

Exercise 3.3.3

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