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#1 2012-09-12 11:59:50

mrpace
Member
Registered: 2012-08-16
Posts: 27

can anyone do this?

Show that if  {v1 , v2} is an orthogonal basis of a vector space V, and x=c1v1 + c2v2 for any real V, then ci = <x, vi>

this seems super hard to me.

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#2 2013-04-13 06:27:28

Nehushtan
Member
From: London
Registered: 2013-03-09
Posts: 602
Website

Re: can anyone do this?

This is only true if the basis is orthonormal (not just orthogonal), i.e.
and
.

Similarly

.

Last edited by Nehushtan (2013-04-13 06:33:44)


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