# Thread: what does this mean??

1. ## 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?

2. Originally Posted by pandakrap
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.

3. ## 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

4. Originally Posted by pandakrap
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?