- #1
teddyayalew
- 36
- 0
Homework Statement
An inner product is linear in both components.
Homework Equations
<x,y> = <conjugate(y),conjugate(x)>
<x+y,z> = <x,z> +<y,z>
The Attempt at a Solution
I thought it was true . It is obvious that it is linear for the first component by definition
Attempt to show it is for second component:
<x,y+z> = <conjugate(y+z),conjugate(x)>
=<conjugate(y),conjugate(x)> + <conjugate(z),conjugate(x)>
= <x,y> + <x,y>
But the answer is false. I am having trouble understanding why it is not linear in both components. The answer key says that the second component is conjugate- linear.