投影矩阵

MATRIX OF PROJECTION

本文主要根据线性方程组的理论给出了求解投影矩阵的方法,再根据投影矩阵与广义逆矩阵之间的关系,进一步又给出了一类广义逆矩阵的求解方法,即满足Penvose’s第一条与第三条广义逆矩阵的一般表达式。

On the basis of iinear equations, the first two parts of the paper give the analytical expression of oblique projection and orthogonal projection of vector in subspace. Cousequently, the definitions of the matrix of oblique projection and the matrix of orthogonal projection hove been drawn; besides, the besic properties of them and the way to find a solution to the mataix of orthogonal projection have been discussed.In the third part, according to the equinalence relation between the matrix of orthogonal projection and the generalized inverse matrix which can content Penr-ose's 1st and 3rd article, and on the basis of the theory of linear ecuations, the general expression of soluing this generalized irnerse matrix has been given.