How do I find orthogonal projections on subspaces?

[Niles]

[SOLVED] Projections on subspaces

Homework Statement

I have some questions on this topic:

1) If I have an orthonormal basis for a subspace U and I have a vector A, and I want to find the orthogonal projection of A onto U, then I use the expression written here:

http://mathworld.wolfram.com/VectorSpaceProjection.html

2) If I have found the orthogonal complement V to U, and I wish to find the projection of the vector A onto V, I can either:

- use the expression in http://mathworld.wolfram.com/VectorSpaceProjection.html on the orthonormal set that spans V

- or use A - proj(U)_A (the projection of A onto U)

3) I don't know if this is "legal", but I would like to draw your attention to my question in: https://www.physicsforums.com/showthread.php?t=207060

The Attempt at a Solution

Can you guys confirm this? Sadly, in my book it is not written that well.

Thanks in advance,

sincerely Niles.

 

[Dick]

Yes, that's correct.

 

[Niles]

Thanks!