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Homework Help: Power method to rank baseball teams

  1. Mar 31, 2012 #1
    Use the power method to rank the baseball league with the matrix

    { 1, .5, .5}
    {.5, 1, 1/3}
    {.5, 2/3, 1}

    So I choose some random matrix which sum to one so
    let x={.5,.3,.2}^T


    { 1, .5, .5}
    {.5, 1, 1/3} {.5,.3,.2}^T= X[itex]_{1}[/itex]
    {.5, 2/3, 1}

    And I keep repeating this scaling the new x vector. Is there an easier way to do this or does it have to be done with technology?
  2. jcsd
  3. Mar 31, 2012 #2


    User Avatar
    Science Advisor
    Homework Helper

    So you want to compute matrix powers of a vector? The usual way to do this is to find the eigenvalues and eigenvectors of the 3x3 matrix and express the vector as a sum of eigenvectors. If you are just making up the numbers, you might find it's pretty hard to find the eigenvectors, though.
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