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Math Help - what does this mean??

  1. #1
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    what does this mean??

    what does it mean, when you say T is in the linear transformation from V to W??

    is T a vector? or is T something else?
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  2. #2
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    Quote Originally Posted by pandakrap View Post
    what does it mean, when you say T is in the linear transformation from V to W??

    is T a vector? or is T something else?
    It means T is a function T: V\to W which satisfies the proporties for being a linear transformation.
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  3. #3
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    thanks just one more thing

    i know that the range of T in T:V to W is = Tv: (v in V)
    and for some tranformation to be surjective, the Range of T has to equal to W, but shouldn't all RangeT should be equal to W??

    could I get some examples of a surjective transformation and an explanation on why??

    thank you
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  4. #4
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    Quote Originally Posted by pandakrap View Post
    Could I get some examples of a surjective transformation and an explanation on why??
    Consider the mapping T:R^3  \mapsto R^2 \,,\,T\left[ \begin{gathered}<br />
  a \hfill \\  b \hfill \\  c \hfill \\ \end{gathered}  \right] = \left[ \begin{gathered}<br />
  a + b \hfill \\  c - b \hfill \\ \end{gathered}  \right]
    In that a linear mapping?

    If \left[ \begin{gathered}  x \hfill \\  y \hfill \\ \end{gathered}  \right] \in R^2 \,\& \,T\left[ \begin{gathered}  x \hfill \\  0 \hfill \\  y \hfill \\ \end{gathered}  \right] = ?.
    What does that tell you about surjectivity?
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