Re: Prove ||u-v|| = 2^(1/2)

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**page929** I need to prove that ||u-v|| = 2^(1/2) if {u,v} is an orthonormal set in the vector space V.

$\displaystyle \|u-v\|^2=(u-v)\cdot (u-v)=u\cdot u-2u\cdot v+v\cdot v=~?$

Re: Prove ||u-v|| = 2^(1/2)

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**Plato** $\displaystyle \|u-v\|^2=(u-v)\cdot (u-v)=u\cdot u-2u\cdot v+v\cdot v=~?$

u^2 - 2uv + v^2

||u||^2 - 2uv + ||v||^2

Re: Prove ||u-v|| = 2^(1/2)

the fact that {u,v} is an orthonormal set tells you you have "special values" for <u,u>, <u,v> and <v,v>. what are they?

Re: Prove ||u-v|| = 2^(1/2)

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Originally Posted by

**Deveno** the fact that {u,v} is an orthonormal set tells you you have "special values" for <u,u>, <u,v> and <v,v>. what are they?

<u,u> = 1, <u,v> = 0, <v,v> = 1

So, 1+0+1 = 2

but I need ||u-v|| not ||u-v||^2, so I take the square root and my answer is 2^(1/2)