anonymous
  • anonymous
Given a basis for the subpace H, if it's not an orthogonal set what can you do in order to make it an orthogonal set or is that not possible?
Mathematics
katieb
  • katieb
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anonymous
  • anonymous
It is possible :D do you know the gram-schimdt process?
anonymous
  • anonymous
(depending) you could also simply multiplly each vector in the base by its magnitude
anonymous
  • anonymous
Oh my prof skipped that chapter hahaha

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anonymous
  • anonymous
Ill learn it later. If she didnt teach it its probably not going to be in a test. You can post a useful link if you would like I'll read it later. Thanks!
anonymous
  • anonymous
it goes like this, suppose we are given a basis B={v1,v2,..,vn}. Now to make this an orthogonal set of vectors which we will call O={u1,u2,..,un}, we do the following: let u1=v1 now let W={u1} so we know that component v2 orthogonal to W(hence orthogonal to all vectors in it)=v2-orthogonal projection of v2=v2-u1/norm(u1)^2 and that will give us u1 so u2=v2-u1/norm(u1)^2 for u3, let W={u1,u2} so the component of v3 orthogonal to W=v3-u1/norm(u1)^2-u2/norm(u2)^2 continue this process till vn now you can see the pattern already right? so to construct an orthogonal basis O={u1,u2,...,un} given a basis B={v1,v2,...,vn}, we do the following: u1=v1 u2=v2-u1/norm(u1)^2 u3=v3-u1/norm(u1)^2-u2/norm(u2)^2 continue this process till we get to: un=vn-u1/norm(u1)^2-u2/norm(u2)^2-...-un-1/norm(un-1)^2 only the norm is squared. the 's are just inner products.
anonymous
  • anonymous
and that will give us u2* correction :))

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