A New Theorem of Projection and Its Application to Adjustment

This paper extends the concept of projection in inner product space, defines the projection of an arbitrary vector in this space onto a linear submanifold and proves the new theorem of projection associated with the definition. On the basis of the formulated definition and proved theorem as well as relevant knowledge of differential geometry, some formulas for adjustment are derived from the point of view of manifold.In addition, the present paper discusses the possibility of the application of "projective method" to solving problems of nonlinear model for adjustment.