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]

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- Apr 12th 2010, 10:17 AMnicolem1051Find 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 PMdwsmith
The projection operator is:

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