Results 1 to 2 of 2

Math Help - FInding a transition matrix

  1. #1
    Junior Member
    Joined
    Mar 2007
    Posts
    40

    FInding a transition matrix

    I know how to do this when the identity matrix is involved but not otherwise. For example can I get a step-by-step process of how this is done:

    Let B = [u1, u2] and B' = [v1, v2] in R2 where
    u1 = [ 2 3] u2 = [ 4 -1] v1 = [ 1 3] v2 = [-1 -1]

    a) Find transition matrix from B' to B
    and
    b) Find transition matrix from B to B'
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Behold, the power of SARDINES!
    TheEmptySet's Avatar
    Joined
    Feb 2008
    From
    Yuma, AZ, USA
    Posts
    3,764
    Thanks
    78
    Quote Originally Posted by chadlyter View Post
    I know how to do this when the identity matrix is involved but not otherwise. For example can I get a step-by-step process of how this is done:

    Let B = [u1, u2] and B' = [v1, v2] in R2 where
    u1 = [ 2 3] u2 = [ 4 -1] v1 = [ 1 3] v2 = [-1 -1]

    a) Find transition matrix from B' to B
    and
    b) Find transition matrix from B to B'
    We need to solve the system for a,b,c,d


    v_1=au_1+bu_2 \mbox{ and } v_2=cu_1+du_2

    or in matrix form we get

    \begin{bmatrix}<br />
2 && 4 && 1 \\<br />
3 && -1 && 3 \end{bmatrix} and \begin{bmatrix}<br />
2 && 4 && -1 \\<br />
3 && -1 && -1 \end{bmatrix}

    a=\frac{13}{14},b=-\frac{3}{14},c=-\frac{5}{14},d=-\frac{1}{14}

    So the transition matrix from B' to B is

     \begin{bmatrix} a && c \\ b && d \end{bmatrix}= \begin{bmatrix} \frac{13}{14} && -\frac{3}{14} \\ -\frac{5}{14} && -\frac{1}{14} \end{bmatrix}

    To find the transition from B to B' reverse the roles of u and v or find the inverse of the matrix above.

    I hope this helps. Good luck.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Transition Matrix
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: March 24th 2010, 02:25 PM
  2. Transition Matrix
    Posted in the Statistics Forum
    Replies: 1
    Last Post: September 5th 2009, 05:37 PM
  3. transition matrix
    Posted in the Advanced Statistics Forum
    Replies: 4
    Last Post: April 23rd 2009, 11:36 PM
  4. transition matrix
    Posted in the Advanced Algebra Forum
    Replies: 0
    Last Post: March 30th 2009, 06:20 PM
  5. transition matrix
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: March 29th 2009, 08:19 PM

Search Tags


/mathhelpforum @mathhelpforum