- #1
yy205001
- 60
- 0
Homework Statement
Let<x,y> be an inner product on a vector space V, and let e1, e2,...,en be an orthonormal basis for V.
Prove: <x,y> = <x,e1><y,e1>+...+<x,en><y,en>.
Homework Equations
<x,x> = abs(x)
a<x,y> = <ax,y> = <x,ay>
The Attempt at a Solution
RHS
=<x,y>
= x1y1+...+xnyn
= x1<e1,e1>y1<e1,e1>+...+xn<en,en>yn<en,en>
* <e,e>=1
=e12<x1,e1>+...+en2<xn,en>
And i cannot find a way to take the e2 out of the equation.
Any help is appreciated