Engineering Analysis/Projections

Projection The projection of a vector onto the vector space is the minimum distance between v and the space W. In other words, we need to minimize the distance between vector v, and an arbitrary vector : Projection onto space W For every vector there exists a vector called the projection of v onto W such that <v-w, p> = 0, where p is an arbitrary element of W. Orthogonal Complement Distance between v and W The distance between and the space W is given as the minimum distance between v and an arbitrary : Intersections Given two vector spaces V and W, what is the overlapping area between the two? We define an arbitrary vector z that is a component of both V, and W: Where N is the nullspace.