Math Is Fun Forum

mrpace

Member

Registered: 2012-08-16

Posts: 88

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.

Nehushtan

Member

Registered: 2013-03-09

Posts: 957

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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