- #1
Niles
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[SOLVED] Projections on subspaces
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
Can you guys confirm this? Sadly, in my book it is not written that well.
Thanks in advance,
sincerely Niles.
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.