# Find orthogonal projection

• Apr 12th 2010, 10:17 AM
nicolem1051
Find orthogonal projection
Find the orthogonal projection of v onto the subspace W spanned by the vectors ui. ( You may assume that the vectors ui are orthogonal.)

v =
[1
2
3]

u1 =
[2
-2
1]

u2 =
[-1
1
4]
• Apr 12th 2010, 07:44 PM
dwsmith
The projection operator is:

$\mathbf{u}_i=\mathbf{v}_i-\sum_{k=1}^{j-1}proj_{\mathbf{u}_k}(\mathbf{v}_j)$