三元方程组Ax=b对应的三种几何意义与应用

Three Geometric Meanings and Applications of 3-demensional System

本文介绍三元线性方程组Ax=b对应的三种几何意义,及其相应的几何应用:(1)方程组中矩阵的秩可用于判断三个平面之间的相对位置;(2)系数矩阵的秩可用于确定列向量组的极大无关组以构成向量空间的坐标架,以及向量的坐标;(3)非奇异矩阵确定仿射变换,可用于图形或图像的仿射变形.

In this paper,we introduce three geometric meanings corresponding to 3-demensional linear system Ax=b and their corresponding geometric applications:(1)The rank of the matrix in the system can be used to determine the relative positions among three planes;(2)The rank of the coefficient matrix can be used to determine a maximal independent group of the column vectors which can form the coordinate frame of the vector space and then determine coordinates of a vector;(3)Affine transformation determined by nonsingular matrix can be used for affine deformation of graph or image.