Derive from $\displaystyle \sum_{k} \vert <x,e_k>\vert ^2 = \|x\|^2$
the following formula which is called the parseval relation:
$\displaystyle <x,y> = \sum_k <x,e_k> \overline{<y,e_k>}.$
Derive from $\displaystyle \sum_{k} \vert <x,e_k>\vert ^2 = \|x\|^2$
the following formula which is called the parseval relation:
$\displaystyle <x,y> = \sum_k <x,e_k> \overline{<y,e_k>}.$