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Derivative of Some Standard Functions

let A=[1 0 1 ...

Question

let A=[1 0 1 1] and P=[ cos pi/6 sin pi/6 -sinpi/6 cospi/6] and Q=PAP^T then P^TQ^2013P

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A = [\begin{matrix} 1 & 1 0 & 1 \end{matrix}]

P = ⎡ ⎢ ⎢ ⎣ \begin{matrix} cos \frac{π}{6} & sin \frac{π}{6} - sin \frac{π}{6} & cos \frac{π}{6} \end{matrix} ⎤ ⎥ ⎥ ⎦

Q = P {A P}^{T},

P^{T} Q^{2021} P

A = [\begin{matrix} 1 & 1 0 & 1 \end{matrix}]

P = [\begin{matrix} cos \frac{π}{6} & sin \frac{π}{6} - sin \frac{π}{6} & cos \frac{π}{6} \end{matrix}],

Q = P A P^{T}

P^{T} Q^{2013} P

{⎛ ⎜ ⎜ ⎝ \frac{1 + cos \frac{π}{6} - i sin \frac{π}{6}}{1 + cos \frac{π}{6} + i sin \frac{π}{6}} ⎞ ⎟ ⎟ ⎠}^{6}

z = 1 + cos \frac{6 π}{5} + i sin \frac{6 π}{5}

{⎡ ⎢ ⎢ ⎢ ⎢ ⎣ \frac{sin \frac{π}{6} + i (1 - cos \frac{π}{6})}{sin \frac{π}{6} - i (1 - cos \frac{π}{6})} ⎤ ⎥ ⎥ ⎥ ⎥ ⎦}^{2}

i = \sqrt{- 1}

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