% These slides are designed for 52 x 19 terminals % but should work with slightly larger or smaller % terminals. Should be OK with unix "less" and % screens with fewer than 30 lines. Issue /%%etc. % Start at lines 10, 40, 70, 100, etc.; use % vi "set number" and "set nonumber" % line 10: s1%%etc., line 40: s2%%etc., etc. % unix, vi, less -- old school! s0%%% Today: Similar matrices: A and B are similar if B = P^(-1) A P . Then B^n = P^(-1) A^n P for any n. (See Wikipedia: Matrix similarity) Diagonalize [1/2,1/3;1/2,2/3] (HW 1) you should make sure that you can do this with any reasonable 2 x 2 matrix. For an algorithm, see 3,000 Solved ..., Section 16.3. Markov or stochastic matrices. See also Subsections 4.6.1 and 4.6.2. s00%%% Announcements: Homework #1 is set: Problem 1 due Sept 16. Problems 2-6 due one week from when ugrad lab accounts are set up. Please hand in Probs 2-6 on Sept 16 if you can. s8%%% - We need to "review" - Markov matrices - Given (Markov) matrix, A how "to find" A, A^2, A^3,... A^infinity i.e., limit as n-> infty of A^n