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Linear transformations

  1. Sep 8, 2013 #1
    Say I have a linear transformation T:V##\rightarrow##W. Can I necessarily say that T(V)##\subseteq##W?

    I feel like T being a linear transformation would make the function behave enough to force things to not be undefined but I can't be certain..
     
  2. jcsd
  3. Sep 8, 2013 #2

    verty

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    Of course. T(V) is the range which is always a subset of the codomain.
     
  4. Sep 8, 2013 #3
    Hmm. I see. Thanks! I'm losing my mind.
     
  5. Sep 8, 2013 #4

    verty

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    Do you understand that this is true for any function ever? That is how functions are defined, the range is a subset of the codomain.
     
  6. Sep 8, 2013 #5
    Yea. I messed up my reasoning with the range and the domain. I switched them around thinking that if something was undefined then it wouldn't be in the range. Like if x=0 and f(x)=1/x then 1/0 is not in the range but it is x=0 that is not in the domain.
     
  7. Sep 16, 2013 #6

    Any mapping ever, really.
     
  8. Sep 16, 2013 #7

    verty

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    I still have the old mindset where every collection is a set and every mapping is a function. Probably this is from reading books not much more recent than the 60's.
     
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