第一个矩阵旋转矩阵
A = R 1 0 0 1 A=\left\\begin{matrix}R_{1} \& 0\\\\0 \& 1\\end{matrix}\\right A=R1001
第一个平移矩阵
B = 1 T 1 0 1 B=\left\\begin{matrix}1 \& T_{1}\\\\0 \& 1\\end{matrix}\\right B=10T11
C = R 2 0 0 1 C=\left\\begin{matrix}R_{2} \& 0\\\\0 \& 1\\end{matrix}\\right C=R2001
两个矩阵的乘积
A B = R 1 R 1 T 1 0 1 AB=\left\\begin{matrix}R_{1} \& R_{1} T_{1}\\\\0 \& 1\\end{matrix}\\right AB=R10R1T11
B A = R 1 T 1 0 1 BA=\left\\begin{matrix}R_{1} \& T_{1}\\\\0 \& 1\\end{matrix}\\right BA=R10T11
B A B C = R 1 R 2 R 1 T 1 + T 1 0 1 BABC=\left\\begin{matrix}R_{1} R_{2} \& R_{1} T_{1} + T_{1}\\\\0 \& 1\\end{matrix}\\right BABC=R1R20R1T1+T11
( B A B C ) − 1 = 1 R 1 R 2 − T 1 R 2 − T 1 R 1 R 2 0 1 (BABC)^{-1}=\left\\begin{matrix}\\frac{1}{R_{1} R_{2}} \& - \\frac{T_{1}}{R_{2}} - \\frac{T_{1}}{R_{1} R_{2}}\\\\0 \& 1\\end{matrix}\\right (BABC)−1=R1R210−R2T1−R1R2T11
我们可以看到，对于齐次矩阵中包含了旋转操作。取前三行和前三列就是旋转矩阵。