PART 11-GEOMETRIC PROJECT?ONS In this part, we shall describe projections geometrically, and show some other related results. Suppose that E is the direct sum E-FeG of two subspaces G. From PROBLEM 2, recall that every u e E can be decomposed uniquely as u v+w,v eF and w E G. We can say that v (respectively w) is the F-component (resp. G-component) of u e E. The projection onto F along G is the function p : E-+ E which takes a vector ? E E to its F-component, then denoted here p(u). In this part, p denotes such a function F and (a) When E R2, and F,G are two non parallel lines through 0, draw a picture of plu) when u e F u G and ue E without being in F nor G
Show transcribed image textPART 11-GEOMETRIC PROJECT?ONS In this part, we shall describe projections geometrically, and show some other related results. Suppose that E is the direct sum E-FeG of two subspaces G. From PROBLEM 2, recall that every u e E can be decomposed uniquely as u v+w,v eF and w E G. We can say that v (respectively w) is the F-component (resp. G-component) of u e E. The projection onto F along G is the function p : E-+ E which takes a vector ? E E to its F-component, then denoted here p(u). In this part, p denotes such a function F and (a) When E R2, and F,G are two non parallel lines through 0, draw a picture of plu) when u e F u G and ue E without being in F nor G