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

Quote:

Originally Posted by

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

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

Quote:

Originally Posted by

**Plato**

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)

Quote:

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)