# $| \langle a , i \rangle| \leq \| a\|$ if $\|i\|=1$ this space is a normed vector space upon $\langle , \rangle$ . Why does this apply?

I tried over Cauchy Schwarz to conclude, but could not. Anyone see why this is ? The term: normed vector space upon $\langle , \rangle$ i hear for the first time, Im assuming it means that: $$\|a \| = \sqrt{ \langle a,a \rangle}$$

• What was the issue you encountered with Cauchy—Schwarz? (as for the definition: yes, it is correct.) – Clement C. Aug 8 '15 at 14:28

Of course that Cauchy Schwarz works ! $$\left<a,i\right>\underset{C.S.}{\leq} \|a\|\underbrace{\|i\|}_{\leq 1}\leq \|a\|$$