平面坐标系变换

平面坐标系变换
flyfish

$$x^{\prime }=x\cos \theta +y\sin \theta$$
$$y^{\prime }=-x\sin \theta +y\cos \theta$$
矩阵形式
$$\left(\begin{array}{c}{x}^{\prime }\\ y^{\prime }\end{array}\right)=\left(\begin{array}{cc}\cos \theta & \sin \theta \\ -\sin \theta & \cos \theta \end{array}\right)\left(\begin{array}{c}x\\ y\end{array}\right)$$

另一种形式
$$x=x^{\prime }\cos \theta -y^{\prime }\sin \theta$$
$$y=x^{\prime }\sin \theta +y^{\prime }\cos \theta$$
矩阵形式
$$\left(\begin{array}{c}x\\ y\end{array}\right)=\left(\begin{array}{cc}\cos \theta & -\sin \theta \\ \sin \theta & \cos \theta \end{array}\right)\left(\begin{array}{c}{x}^{\prime }\\ y^{\prime }\end{array}\right).$$