1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Linear Operator

  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

    User Avatar
    Science Advisor
    Homework Helper

    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

    User Avatar
    Science Advisor
    Homework Helper

    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.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Linear Operator
  1. Linear operator (Replies: 1)

  2. Linear Operator (Replies: 25)

  3. Linear operators (Replies: 2)

  4. Linear operator (Replies: 1)

  5. Linear Operator (Replies: 21)

Loading...