Power method to rank baseball teams

[Punkyc7]

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


So

{ 1, .5, .5}
{.5, 1, 1/3} {.5,.3,.2}^T= X$_{1}$
{.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?

 

[Dick]

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.