Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

I How this defines a linear transformation

  1. Apr 25, 2016 #1
    Admit that [tex]V[/tex] is a linear space about [tex]\mathbb{R}[/tex] and that U and W are subspaces of V. Suppose that [tex]S: U \rightarrow Y[/tex] and [tex]T: W \rightarrow Y[/tex] are two linear transformations that satisfy the property:

    [tex](\forall x \in U \cap W) S(x)=T(x)[/tex]

    Define a linear transformation [tex]F: U+W \rightarrow Y[/tex] that matches with S for values in U and matches with T with values in W.

    My thought is to choose the linear transformation [tex]F=S+T[/tex] because it will be the union of both transformation, right? But we have the problem that when our objects are in the intersection of both space we will get to F = 2S instead of S
     
    Last edited: Apr 25, 2016
  2. jcsd
  3. Apr 25, 2016 #2

    Stephen Tashi

    User Avatar
    Science Advisor

    On this forum the tags using backslash and "tex" don't work for LaTex. Use a forward slash.

    Are you asking whether it is possible to define such a linear transformaton ?

     
  4. Apr 25, 2016 #3
    Hello Stephen!

    Thanks, I edited my question.

    No, I know it's possible to define the linear transformation I'm asking what should be the linear transformation and how can I get there :)
     
  5. Apr 25, 2016 #4

    jbunniii

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Do you know about direct sums, and complements of subspaces?
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted