1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Linear Transformations

  1. Apr 13, 2004 #1
    I'd like to check my proof. It seems easy enough, but I'd like to make sure that I'm not missing anything:

    If V is the space of all continuous functions on [0,1] and if
    Tf = integral of f(x) from 0 to 1 for f in V, show that T is a linear transformation From V into R1.

    Like I said the proof seems simple enough, but I just want to make sure I'm not missing anything that might be implied by "From V into R1."

    T(f + g) = integral from 0 to 1[f(x) + g(x)]dx
    = integral from 0 to 1 f(x)dx + integral from 0 to 1 g(x)dx
    = Tf + Tg

    T(kf) = integral from 0 to 1 kf(x)dx
    = k*integral from 0 to1 f(x)dx
    = kTf

    there for T is a linear transformation.

    I feel silly posting something this simple, but I'm just not absolutely sure that I'm not missing something.

    Thanks as usual for all the help.
     
  2. jcsd
  3. Apr 14, 2004 #2
    Yeah, that looks fine.

    [tex]f:V \rightarrow\ R[/tex] just refers to the fact that the definite integral over a function in V will always give you a constant real number.
     
  4. Apr 14, 2004 #3
    Thanks Stevo.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Linear Transformations
  1. Linear transformations (Replies: 0)

  2. Linear Transformation (Replies: 6)

  3. Linear transformation (Replies: 6)

  4. Linear Transformations (Replies: 0)

Loading...