Linear transformations

  • #1
274
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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..
 

Answers and Replies

  • #2
verty
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Of course. T(V) is the range which is always a subset of the codomain.
 
  • #3
274
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Hmm. I see. Thanks! I'm losing my mind.
 
  • #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.
 
  • #5
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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.
 
  • #6
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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.

Any mapping ever, really.
 
  • #7
verty
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Any mapping ever, really.
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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