anonymous
  • anonymous
Hi. Im looking for the formula to calculate the orthogonal projection of w onto the subspace spanned by u and v. Where W,U,V are vectors
Mathematics
schrodinger
  • schrodinger
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amistre64
  • amistre64
would that be the cross product of u and v?
amistre64
  • amistre64
or rather, if they exist all inthe same subspace and are orthogonal; then wouldnt the dot products betweenthem be zero?
amistre64
  • amistre64
orthogonal projection...... eh...

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amistre64
  • amistre64
i dont know the formula, but it sounds intriguing ;)
anonymous
  • anonymous
here is a simple example that may help
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amistre64
  • amistre64
lol..you said it was simple :)
anonymous
  • anonymous
The vectors themselves are as follows u = 1 over the square root of 2 [-1] [ 0] [1] v = 1 over the square root of 6 [1
anonymous
  • anonymous
v = 1 over the square root of 6 [1 ] [-2] [1] w = [2] [1] [-3]
anonymous
  • anonymous
There is a formula for orthogonal projection but it is usually used between two vectors, you would have to figure out how to use it with a third. For example orthogonal projection of v on u is [(v dot u)/||u||^2]multiplied by vector u

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