Dear Colleagues,

Could you please help me in solving the following problem:

Show that in an inner product space, $\displaystyle x\bot y$ if and only if $\displaystyle ||x+\alpha y||\geq ||x||$ for all scalars $\displaystyle \alpha$.

Remark: I have already proved that $\displaystyle x\bot y$ implies that $\displaystyle ||x+\alpha y||\geq ||x||$ for all scalars $\displaystyle \alpha$, it remains the converse.

Regards,

Raed.