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Homework Help: Complex conjugate operator is linear

  1. Oct 16, 2011 #1
    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?
     
  2. jcsd
  3. Oct 16, 2011 #2

    Dick

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    If a function is linear then f(cx)=c*f(x). Right? Put c=i and f to be complex conjugation.
     
  4. Oct 16, 2011 #3
    I thought that the definition of a linear operator was:

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

    (where A is a linear operator)
     
  5. Oct 16, 2011 #4

    Dick

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    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.
     
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