In case someone is interested in the "eigenanalysis," the recursion formula is: [1/2, 1/2, 0 ] [A^n] [A^n+1] [1/8, 3/4, 1/8] [B^n] = [B^n+1]

In case someone is interested in the "eigenanalysis," the recursion formula is: [1/2, 1/2, 0 ] [A^n] [A^n+1] [1/8, 3/4, 1/8] [B^n] = [B^n+1] [0, 1/2, 1/2] [C^n] [C^n+1] \_____ _____/ M And the question is, given [A^0,B^0,C^0], find [A^∞,B^∞,C^∞], which is equivalent to computing the infinite power of M. Waaaat? Enter the eigendecomposition. The eigenvalues of M are 1/4, 1/2, and 1. If you compute M^∞, the 1/4 and 1/2 "eigenspaces" will disappear, so you're left with the subspace of the eigenvalue 1. http://bit.ly/eigenex001 http://bit.ly/eigenex001 M^∞ = QL^∞Q.inv(), hence the [1,4,1] appears... very cool. Sometimes procrastinating by reading HN actually helps with your work---today I'm working on problem sets for book 2 http://gum.co/noBSLA http://gum.co/noBSLA