Results 1 to 4 of 4

Thread: what does this mean??

  1. #1
    Junior Member
    Joined
    Nov 2008
    Posts
    41

    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?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    10
    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 $\displaystyle T$ is a function $\displaystyle T: V\to W$ which satisfies the proporties for being a linear transformation.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Nov 2008
    Posts
    41

    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
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Aug 2006
    Posts
    21,776
    Thanks
    2823
    Awards
    1
    Quote Originally Posted by pandakrap View Post
    Could I get some examples of a surjective transformation and an explanation on why??
    Consider the mapping $\displaystyle T:R^3 \mapsto R^2 \,,\,T\left[ \begin{gathered}
    a \hfill \\ b \hfill \\ c \hfill \\ \end{gathered} \right] = \left[ \begin{gathered}
    a + b \hfill \\ c - b \hfill \\ \end{gathered} \right]$
    In that a linear mapping?

    If $\displaystyle \left[ \begin{gathered} x \hfill \\ y \hfill \\ \end{gathered} \right] \in R^2 \,\& \,T\left[ \begin{gathered} x \hfill \\ 0 \hfill \\ y \hfill \\ \end{gathered} \right] = ?$.
    What does that tell you about surjectivity?
    Follow Math Help Forum on Facebook and Google+


/mathhelpforum @mathhelpforum