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Are these two linear maps equivalent?

  1. Apr 10, 2012 #1
    let S: A ->B and T: B -> C be linear maps.
    Then
    TS : A -> B -> C.
    But am I right in thinking that the map T': Im(A) -> C is the same as TS?

    If this is wrong, can you explain why please :)

    Thanks very much in advance!
     
  2. jcsd
  3. Apr 10, 2012 #2

    micromass

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    What is Im(A)?
     
  4. Apr 10, 2012 #3
    My guess would be imaginary part.
     
  5. Apr 10, 2012 #4
    Im(A) is Image(A) or the space that we get when we apply the linear transformation S to A.
    Also T' is the same transformation as T but just on a different domain.

    I guess what I wrote in OP was wrong, but is it fine to say that Image(T') = Image(TS),
    so Rank(T') = Rank(TS) ?
     
  6. Apr 10, 2012 #5

    micromass

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    The correct notation is Im(S) or S(A). The notation Im(A) is not in use.
    That is indeed correct.
     
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