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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?
 one year ago
 one year ago
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?
 one year ago
 one year ago

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anonymoustwo44Best ResponseYou've already chosen the best response.1
It is possible :D do you know the gramschimdt process?
 one year ago

LagrangeSon678Best ResponseYou've already chosen the best response.0
(depending) you could also simply multiplly each vector in the base by its magnitude
 one year ago

RomeroBest ResponseYou've already chosen the best response.0
Oh my prof skipped that chapter hahaha
 one year ago

RomeroBest ResponseYou've already chosen the best response.0
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!
 one year ago

anonymoustwo44Best ResponseYou've already chosen the best response.1
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)=v2orthogonal projection of v2=v2<v2,u1>u1/norm(u1)^2 and that will give us u1 so u2=v2<v2,u1>u1/norm(u1)^2 for u3, let W={u1,u2} so the component of v3 orthogonal to W=v3<v3,u1>u1/norm(u1)^2<v3,u2>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<v2,u1>u1/norm(u1)^2 u3=v3<v3,u1>u1/norm(u1)^2<v3,u2>u2/norm(u2)^2 continue this process till we get to: un=vn<vn,u1>u1/norm(u1)^2<vn,u2>u2/norm(u2)^2...<vn,un1>un1/norm(un1)^2 only the norm is squared. the <u,v>'s are just inner products.
 one year ago

anonymoustwo44Best ResponseYou've already chosen the best response.1
and that will give us u2* correction :))
 one year ago
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