Results 1 to 3 of 3

Math Help - What does "complex linear" mean?

  1. #1
    Junior Member
    Joined
    Feb 2011
    Posts
    34

    What does "complex linear" mean?

    This question says to regard the set of complex numbers as a vector space V over the reals

    and to find a linear transformation V to V which is not complex linear.

    What does complex linear mean?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Mar 2011
    From
    Tejas
    Posts
    3,392
    Thanks
    759

    Re: What does "complex linear" mean?

    the complex numbers are also a field, so we have 2 choices for regarding them as a vector space:

    1) as a vector space over the complex field, of dimension 1, with basis {1}
    2) as a vector space over the real field, of dimension 2, with basis {1, i}.

    you are being asked to find a mapping which is linear in the sense of (2), but not in the sense of (1).
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Feb 2011
    Posts
    34

    Re: What does "complex linear" mean?

    Thanks for answering

    so the transformation that sends

    (x,y) to (x,y) doesn't not work because that's the same thing as

    (x+iy)*1 or x*1+y*i

    Why does complex conjugation work though?

    isn't \bar{z} both

    \bar{z}*1

    x*1+-y*i
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 3
    Last Post: October 17th 2011, 02:50 PM
  2. Replies: 1
    Last Post: September 16th 2011, 01:08 AM
  3. Replies: 2
    Last Post: April 24th 2011, 07:01 AM
  4. Replies: 1
    Last Post: October 25th 2010, 04:45 AM
  5. Replies: 1
    Last Post: June 4th 2010, 10:26 PM

Search Tags


/mathhelpforum @mathhelpforum