Two vectors u, v are orthogonal if and only if ||u+v||^2 +||u-v||^2 = 2||u||^2 - 2||v||^2? Doesn't (u+v)(u+v) + (u-v)(u-v) = u^2 + v^2?
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edited for stupidity
Good question man, I don't see how orthogonality plays any role. $\displaystyle ||u+v||^2+ ||u-v||^2=(u+v)\cdot(u+v)+(u-v)\cdot(u-v) $ $\displaystyle ||u||^2+u\cdot v + v\cdot u +||v||^2 + ||u||^2-u\cdot v - v\cdot u +||v||^2 = 2||u||^2+2||v||^2$
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