1. Limited time only! Sign up for a free 30min personal 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 transformation

  1. Jul 20, 2010 #1
    I'm hoping I can get some help with the following question:

    Does definite integration (from x = 0 to x = 1) of functions in Pn correspond to some linear transformation from Rn+1 to R?

    OK, well my original answer was yes, but the textbook says "no, except for P0" which I do not understand.

    So I have p(x) = anxn + an-1xn-1 + ... + a1x + a0

    If I integrate from 0 to 1, I get: P(1) = an/(n+1) + an-1/n + ... + a1/2 + a0

    Right?

    So I have T(an, an-1, ..., a1, a0) = (an/(n+1) + an-1/n + ... + a1/2 + a0)

    and T: Rn+1 -> R

    And if I want to show that it is linear, then I show that the transformation has these properties:
    T(kx) = kT(x) and
    T(x+y) = T(x) + T(y)
    and I think both cases are obvious.

    And T is multiplication by [1/(n+1) | 1/n . . . 1/2 | 1]

    What am I missing?
    Thanks in advance for any help.
     
  2. jcsd
  3. Jul 20, 2010 #2

    hunt_mat

    User Avatar
    Homework Helper

    Linear transformations usually mean between vector spaces of the same dimension and therefore can be loosely thought of as matrices. what you have is a linear functional.

    Mat
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Linear transformation
  1. Linear Transformation (Replies: 1)

  2. Linear transformations (Replies: 4)

  3. Linear transformation (Replies: 4)

  4. Linear transformation (Replies: 18)

Loading...