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Finding the transition matrix

  1. Mar 23, 2017 #1
    1. The problem statement, all variables and given/known data
    Let ##B_1 = {\begin{bmatrix} 1 \\ 1 \\ 1\\ 0 \end{bmatrix}}, {\begin{bmatrix} 1 \\ 1 \\ 0\\ 0 \end{bmatrix}}, {\begin{bmatrix} 0 \\ 0 \\ 1\\ 1 \end{bmatrix}} ## and ##B_2 = {\begin{bmatrix} 1 \\ 1 \\ 1\\ 1 \end{bmatrix}}, {\begin{bmatrix} 1 \\ 1 \\ 1\\ -1 \end{bmatrix}}, {\begin{bmatrix} 1 \\ 1 \\ -1\\ 1 \end{bmatrix}}## be two bases for ##span(B_1)##, where the usual left to right ordering is assumed. Find the transition matrix ##P##B1##\to##B2

    2. Relevant equations


    3. The attempt at a solution
    I'm a bit flummoxed here. All the problems I've dealt with so far have had ##n## ##n \times 1## vectors and were solved by finding inverses. That cannot work here. What would be the first step in solving this?
     
  2. jcsd
  3. Mar 23, 2017 #2

    PeroK

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    You could express one set of basis vectors in terms of the other basis.
     
  4. Mar 23, 2017 #3
    Would you happen to know how to get formulas to display correctly on an android phone? I'm away from my pc for a spell and I can't see much this way.
     
  5. Mar 23, 2017 #4

    Math_QED

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    The first step: know the relevant definitions and theorems

    If you want to find the transition matrix, you have to know what information can be found within it. In general, a transition matrix gives you all the information you need to know to convert coordinates of a certain basis to coordinates relative to another basis. Denote the transition matrix from ##B_1## to ##B_2## with ##M##. Do you know what information you can find in the columns of ##M##?
     
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