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!

Annihilator proof

  1. Oct 24, 2009 #1
    Let W1 and W2 be subspaces of a finite dimension.
    Prove that A(W1 intersection with W2) = A(W1) + A(W2)
    Where A(W1) is the annihilator of W1.
    I can prove one way, but not the other. How do I prove the rhs is contained in the lhs?
     
  2. jcsd
  3. Oct 24, 2009 #2
    Try to find the dimension of A(W1) + A(W2) and A(W1 intersect. W2) to show that they are the same space.
    It will help to show that [A(W1) intersect. A(W2)] = A(W1 + W2)
     
  4. Oct 24, 2009 #3

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    If you have an operator 'a' that vanishes on W1 intersect W2, then you have have to construct two operators a1 in A(W1) and a2 in A(W2) such that a=a1+a2. I'd suggest you pick an appropriate basis for W1+W2.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Annihilator proof
  1. Annihilator method (Replies: 8)

  2. Annihilator method (Replies: 2)

Loading...