Results 1 to 2 of 2

Math Help - Composition of Linear Transformations (2)

  1. #1
    Junior Member
    Joined
    Sep 2008
    Posts
    28

    Composition of Linear Transformations (2)

    Let V be a vector space, and let T: V-> V be linear. Prove that T^2 = T0 if and only if R(T) is contained in N(T).

    Thanks..
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Junior Member
    Joined
    Oct 2008
    Posts
    64
    Suppose T^2=0
    Let y\in R(T(x)). Then y=T(x) for some x. Now T(y)=T(T(x))=T^2(x)=0. This shows that x\in N(T).

    Conversely let R(T)\subset N(T).
    Then T(x) in N(T) for every x, which implies that T(T(x))=0. Hence T^2=0
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Linear Transformations and the General Linear Group
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: December 26th 2011, 11:50 AM
  2. Basic Linear Algebra - Linear Transformations Help
    Posted in the Advanced Algebra Forum
    Replies: 6
    Last Post: December 7th 2010, 04:59 PM
  3. Composition of Linear Transformations
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: October 11th 2008, 01:44 PM
  4. composition of linear transformation question
    Posted in the Advanced Algebra Forum
    Replies: 0
    Last Post: February 27th 2008, 11:52 PM
  5. Replies: 3
    Last Post: June 2nd 2007, 11:08 AM

Search Tags


/mathhelpforum @mathhelpforum