- #1
Shackleford
- 1,656
- 2
I don't know how to start this problem. Since it's a bi-implication, I need to show each statement implies the other. I started playing around with the definitions of inner product and norm directly, but it's not going anywhere.
http://i111.photobucket.com/albums/n149/camarolt4z28/IMG_20120225_142910.jpg
http://i111.photobucket.com/albums/n149/camarolt4z28/IMG_20120225_142929.jpg
If I expand the inner product on the right,
<T(x),T(y)> = (2/4)<T(x),T(y)> + (2/4)<T(y),T(x)> = <x,y>.
Of course,
[itex]\|\vec{T(x)}\| = \sqrt{<T(x),T(x)>} = \sqrt{<x,x>}[/itex].
http://i111.photobucket.com/albums/n149/camarolt4z28/IMG_20120225_142910.jpg
http://i111.photobucket.com/albums/n149/camarolt4z28/IMG_20120225_142929.jpg
If I expand the inner product on the right,
<T(x),T(y)> = (2/4)<T(x),T(y)> + (2/4)<T(y),T(x)> = <x,y>.
Of course,
[itex]\|\vec{T(x)}\| = \sqrt{<T(x),T(x)>} = \sqrt{<x,x>}[/itex].
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