Transformations that preserves the vector angles?

I read somewhere that normal transformations (hermitian, unitary, orthogonal, etc...) preserves the angles between vectors.

but transformation is a function that operates on **one **vector, not two ($\displaystyle T(v)=w$), so what angle exactly are we talking about here?

Re: Transformations that preserves the vector angles?

Hey Stormey.

I'm not certain but I'm thinking that it means that <Tu,Tv>/|Tu|*|Tv| = <u,v>/|u||v| where <.,.> is an inner product and |.| is a norm = SQRT(<.,.>)

Re: Transformations that preserves the vector angles?

Hi chiro.

thanks for the help.

Re: Transformations that preserves the vector angles?

Yes. Saying that "T preserves angles" means that the angle between Tu and Tv is the same as the angle between u and v.