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Topic: Generalizing Orthogonal Projection
Replies: 7   Last Post: Jan 24, 2013 5:17 PM

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Posts: 134
Registered: 11/12/12
Generalizing Orthogonal Projection
Posted: Jan 22, 2013 12:47 AM
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Hi, All:

I'm just curious about wether orthogonalprojection generalizes to cases such as

Say we have a 1-D subspace L (i.e., a line thru the origin) in R^3 , and
let q=(x,y,z) be a point in R^3 which is not on the line. Then I don't see
how to project q orthogonally onto L; I can see how to project q into a
2-D subspace P : the projection of q into P is the ortho complement, and
every vector in P is in the orthogonal complement of the ortho projected
line. But, the same is not the case with q and L. Sorry for the rambling;
my question is then actually:

If L is a 1-D subspace of R^3, and q=(x,y,z) is a point not on L. Can we
define the orthogonal projection of q into L, or do we need to have a plane
P (as subspace) , to define an ortho projection of q?


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