Thread: Show that in an inner product space

Dear Colleagues,

Could you please help me in solving the following problem:
Show that in an inner product space, if and only if for all scalars .

Remark: I have already proved that implies that for all scalars , it remains the converse.


Regards,

Raed.

Take the squares and expand the inner product.

Thank you very much for your reply, I have already done that and the result is
, where denotes the real part of a complex number.

But what then?

You can divide by .