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!

T-Cyclic Subspaces

  1. Apr 13, 2010 #1
    1. The problem statement, all variables and given/known data
    For each linear operator T on the vector space V, find an ordered basis for the T-Cyclic subspace generated by the vector z.

    a) V = R4, T(a+b,b-c,a+c,a+d) and z= e1

    2. Relevant equations
    Theorem: Let T be a linear operator on a finite dimensional vector space V, and let W denote the T-cyclic subspace of V generated by a nonzero vector v [tex]\epsilon[/tex] V. Let k = dim(w). Then:

    a) {v, T(v), T2(v),..., Tk-1(v)} is a basis for W.


    3. The attempt at a solution
    v= (1,0,0,0), T(v)= (1,0,1,1), T2(v)= T(T(v))= (1,-1,2,2), T3(v)= T(T2(v)) = (0,-3,3,3)

    so basis for W = {(1,0,0,0), (1,0,1,1), (1,-1,2,2), (0,-3,3,3)} ?
     
  2. jcsd
  3. Apr 13, 2010 #2

    lanedance

    User Avatar
    Homework Helper

    the transforms look ok, but the theorem assumes you know k the dimisenion of the T-cyclic subspace generated... how do you know it is 4?

    note that
    -(1,0,1,1) + (1, -1, 2, 2) = (0,-1,1,1)
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: T-Cyclic Subspaces
  1. T-Invariant Subspaces (Replies: 5)

  2. T-Cyclic Subspaces (Replies: 2)

  3. T-invariant subspaces (Replies: 2)

Loading...