矩阵分解在运动分析中的应用初探

Preliminary Application of Matrix Decmposition to Motion Analysis

本文首先建立了矩阵除法的概念,然后给出了一种新的矩阵分解法——梯形分解法,并运用此方法,着重对仿射群A_2(R)和A_3(R)的元素,它们的结构及相互间的运算规律作初步的探讨。结论表明,A_2(R)和A_3(R)的元素可表为一系列代表简单运动的元素的合成,从而剖析了它们的内在结构。

In this paper, the conception of matrix division is set up first. Then a new method of matrix decomposition-trapezoidal decomposition is presented. With this method, an emphasis is given to some preliminary discussions on the affine group elements A2(R), A3(R), their structures,and their operations. The results show that the elements of A2(R), A3(R) are to be a serie of compositions of elements, reprenting simple motion. In this way, their inner motion structure is analyzed.