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!

Determine if a transformation is linear

  1. Oct 26, 2011 #1
    Well, I've done some research on the further, more advanced chapters in my course and learned that these two conditions must be met:

    T(u + v) = T(u) + T(v)
    T(ku) = kT(u)


    I was wondering if there's another way to figure if the transformation is linear (since this question is being asked in one of the "basic" chapters previous to the one mentioning the formulas)

    Thanks!
     
  2. jcsd
  3. Oct 26, 2011 #2
    btw... What would be a good definition for LINEAR TRANSFORMATION?
     
  4. Oct 27, 2011 #3

    BruceW

    User Avatar
    Homework Helper

    search linear map on wikipedia. That gives pretty much the same definition as you have, but they say it a bit more rigorously.
     
  5. Oct 27, 2011 #4

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    The point of what aerozeppelin and Bruce W are saying is that "T(u+v)= T(u)+ T(v)" and "T(ku)= kT(u)" are usually taken as the definition of "linear transformation". And you certainly can't ask whether something is a linear transformation before you have defined it! If your text is asking to determine whether a function is a linear transformation before those formulas are given, what definition is given?
     
  6. Oct 27, 2011 #5
    The first time you get the LINEAR TRANSFORMATION idea in my text, they say:

    " In the special case where the equations in 1 are linear, the transformation
    T: Rn --> Rm defined by those equations is called a linear transformation (or a linear operator if m = n ). "


    And then, the question asked is:
    " Show that the orthogonal projections on the coordinate axes are linear operators, and find their standard matrices"

    How can this be shown?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Determine if a transformation is linear
  1. Linear Transformation (Replies: 4)

  2. Linear transformations (Replies: 21)

  3. Linear Transformation (Replies: 1)

Loading...