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  Discussion about math, puzzles, games and fun.   Useful symbols: √ ∞ ≠ ≤ ≥ ≈ ⇒ ∈ Δ θ ∴ ∑ ∫ π -

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#1 2012-09-13 09:59:50

mrpace
Member

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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.

#2 2013-04-14 04:27:28

Nehushtan
Power Member

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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 (2013-04-14 04:33:44)


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