Complex conjugate operator is linear

[Jimmy25]

My textbook claims that the complex conjugate operator is linear. I can't see how this could be. Could someone give me an example of how it is not linear?

 

[Dick]

My textbook claims that the complex conjugate operator is linear. I can't see how this could be. Could someone give me an example of how it is not linear?

If a function is linear then f(cx)=c*f(x). Right? Put c=i and f to be complex conjugation.

 

[Jimmy25]

I thought that the definition of a linear operator was:

A(f+g)=A(f)+A(g)

(where A is a linear operator)

 

[Dick]

I thought that the definition of a linear operator was:

A(f+g)=A(f)+A(g)

(where A is a linear operator)

That's only part of it. And sure, complex conjugation satisfies that. But you also need A(c*f)=c*A(f), where c is a scalar. That's the part complex conjugation fails.