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 Algebra - proof of transformation

  1. Oct 22, 2012 #1
    1. The problem statement, all variables and given/known data
    Suppose T: V -> W is linear. Prove that T(0) = 0

    3. The attempt at a solution

    T(v) = Av
    T(0) = A(0) = 0

    Is that right?
  2. jcsd
  3. Oct 22, 2012 #2


    User Avatar
    Staff Emeritus
    Science Advisor
    Education Advisor
    2016 Award

    What is A? Why can you write T(v)=Av? What is your definition of linear?
  4. Oct 22, 2012 #3
    A is the transformation matrix. For a transformation T, we need some kind of "transformer" and A is the transformation matrix I used. v is a random vector that is being transformed, in this case it's just the zero vector.
  5. Oct 22, 2012 #4


    User Avatar
    Staff Emeritus
    Science Advisor

    Essentially you are using what you are asked to prove- you can write a linear transformation as a matrix because, among other things, T(0)= 0.

    A linear transformation, T, from vector space U to vector space V, must satisfy
    1) T(u+ v)= T(u)+ T(v) with u and v vectors in U.
    2) T(au)= aT(u) with a a member of the underlying field and u a vector in U.

    Use (1) with v= 0 or (2) with a= 0.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook