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Forum: General Questions - University/Tertiary
Welcome to the General Questions - University/Tertiary forum!
Questions from any subject, at the university/tertiary/4-year college level.
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A proof on orthogonality
by
zee
on 2009-11-25 14:53:30
If V and W are orthogonal subspaces, show that the only vector they have in common is the zero vector: V intersection W={0}. If V and W are orthogonal subspaces then every vector in V is orthogonal to every vector in W. We know that the zero vector is orthogonal to every v in V and every w in W. Can yo give me some feedback ? Thanks and Happy Thanksgiving!
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More on orthogonality
by
zee
on 2009-11-25 14:42:53
Suppose S={0} is the subspace of R^4 containing only the zero vector. Wouldn't the orthogonal complement of S be all of R^4. Can you help me with the following: If S is spanned by ( 0 ,0,0,1), what is the orthogonal complement of S and what is the orthogonal complement of the orthogonal complement of S ? I think the orthogonal complement of Span(0,0,0,1) would be the set of all vectors in R^4 of the form (a,b,c,0). The orthogonal complement of the orthogonal complement of Span(0,0,0,1) would be the set of all vectors in R^4 of the form (x,y,z,d) such that ax+by+cz=0. Is this valid.....I think so.
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Re: More on orthogonality
by Ziosilvio
on 2009-11-25 18:32:03
Help with a proof
by
zee
on 2009-11-25 13:23:04
Show that x-y is orthogonal to x+y iff ||x||=||y||. So I start by assuming x-y is orthogonal to x+y and try to show that their inner product is zero. Can you help me get started. Thanks.
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Re: Help with a proof
by zee
on 2009-11-25 13:57:20
Re: Help with a proof
by Ziosilvio
on 2009-11-25 13:57:46
Re: Help with a proof
by pahio
on 2009-11-25 14:03:32
Re: Help with a proof
by zee
on 2009-11-25 14:22:39
Re: Help with a proof
by mathman
on 2009-11-25 22:42:51
Orthogonality
by
zee
on 2009-11-23 17:26:18
Find all vectors in R^3 that are orthogonal to ( 1 , 1 , 1) and ( 1, -1, 0 ). Produce an orthonormal basis from these vectors (mutually orthogonal unit vectors). Thanks for any feedback.
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Re: Orthogonality
by pahio
on 2009-11-23 19:09:25
Re: Orthogonality
by zee
on 2009-11-24 14:00:42
Re: Orthogonality
by darkgently
on 2009-11-24 15:01:49
Re: Orthogonality
by zee
on 2009-11-25 03:15:20
Article in Mathworld
by
curious
on 2009-11-22 20:03:11
I was reading an article in Wolfram Mathworld about second order differential equations.
Here is the link:
http://mathworld.wolfram.com/Second-OrderOrdinaryDifferentialEquation.html
The author tries to transform (9) into constant coefficients by doing the wierd substitution z=y(x). Note that (d^2 y)/(dz^2) = 0 and dy/dz = 1, adn eq (14) becomes and ALGEBRAIC equation with solution y = -A/B.
Does this mean that there is something wrong?? It seems that the explanation is weak.. What do you think?
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Re: Article in Mathworld
by darkgently
on 2009-11-23 01:23:52
Re: Article in Mathworld
by perucho
on 2009-11-24 18:29:39
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