Given A=(01−10)A = \begin{pmatrix} 0 & 1 \\ -1 & 0 \end{pmatrix}A=(0−110), compute the matrix exponential eAθe^{A\theta}eAθ where θ∈R\theta \in \mathbb{R}θ∈R.
(sinθcosθ−cosθsinθ)\begin{pmatrix} \sin \theta & \cos \theta \\ -\cos \theta & \sin \theta \end{pmatrix}(sinθ−cosθcosθsinθ)
(e0e1e−1e0)\begin{pmatrix} e^0 & e^1 \\ e^{-1} & e^0 \end{pmatrix}(e0e−1e1e0)
(cosθsinθ−sinθcosθ)\begin{pmatrix} \cos \theta & \sin \theta \\ -\sin \theta & \cos \theta \end{pmatrix}(cosθ−sinθsinθcosθ)
(1θ−θ1)\begin{pmatrix} 1 & \theta \\ -\theta & 1 \end{pmatrix}(1−θθ1)