Open main menu

Engineering Analysis/Projections

< Engineering Analysis

ProjectionEdit

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 ComplementEdit

 

Distance between v and WEdit

The distance between   and the space W is given as the minimum distance between v and an arbitrary  :

 

IntersectionsEdit

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.