1. The right spectral radius of every right stochastic matrix is clearly at most 1. 2. My first step is understanding Stochastic matrix . 3. To compute these probabilities the column stochastic matrix " G " is computed such that 4. Since "'P "'is a row stochastic matrix , its largest left eigenvalue is 1. 5. In particular, the k-th power P ^ k of a right stochastic matrix P is also right stochastic. 6. First of all, I was wondering whether what I added would be more appropriately placed in the stochastic matrix article. 7. Thus, each row of a right stochastic matrix ( or column of a left stochastic matrix ) is a stochastic vector. 8. Thus, each row of a right stochastic matrix ( or column of a left stochastic matrix ) is a stochastic vector. 9. A permutation matrix is itself a doubly stochastic matrix , but it also plays a special role in the theory of these matrices. 10. Multiplying together stochastic matrices always yields another stochastic matrix , so "'Q "'must be a stochastic matrix.
