- #1

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consider:

**w**=

**x**+u

**y**(i'll drop the emboldening of vectors now to save time)

0 <= <x,x> + <uy,x> + <x,uy> + <uy,uy>

0 <= <x,x> + u*<y,x> + u<x,y> + u*u<y,y>

Choose u = <y,x>/<y,y>

0 <= <x,x> + (<y,x>/<y,y>)*<y,x> + (<y,x>/<y,y>)<x,y> + (<y,x>/<y,y>)

^{2}<y,y>

some manipulation here concludes the proof.

My question is that by choosing a specific u are we not losing generality?