(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

An inner product is linear in both components.

2. Relevant equations

<x,y> = <conjugate(y),conjugate(x)>

<x+y,z> = <x,z> +<y,z>

3. 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.

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# Homework Help: Linear Algebra: Linearity of inner product

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