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Injective linear tranformations

  1. May 22, 2009 #1
    I was just wondering how you know if linear transformations injective?
     
  2. jcsd
  3. May 22, 2009 #2

    matt grime

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    You work out its kernel. If it's a map from V to V then you can work out its determinant which tells you if the kernel is zero or not (but not what it is).
     
    Last edited: May 22, 2009
  4. May 22, 2009 #3
    thanks
     
  5. May 22, 2009 #4

    HallsofIvy

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    A function, f, in general, is injective if f(x)= f(y) implies x= y. If f is linear, then f(x)= f(y) gives f(x)- f(y)= f(x-y)= 0 while x= y is the same as x- y= 0. That is why a linear function is injective if and only if its kernel is trivial: {0}, as matt grime said.
     
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