How do I create a Markov Matrix with variables instead of numbers for probabilities?

How do I create a Markov Matrix with variables instead of numbers where the probabilities should go?

Answer 1

[Dana]

If your goal is to manipulate P symbolically (i.e., algebraically, rather than numerically), then you'll need to use Matlab's symbolic toolbox if you have it. In that case,

P = sym('p',[4,4]);

creates a symbolic matrix P with element (i,j) denoted by pi_j.

[Khushi Patel]

Thank you so much!

Just wondering, is there any way to sub in values for p1_1, p11_2....pi_j into the matrix?

[Dana]

Use the subs function. To do one element at a time, subs(P,'p1_1',1) would replace p1_1 (which is the (1,1) element of P) with the number 1. To replace the whole matrix in one go with the elements of another matrix:

m = magic(4); % an arbitrary 4-by-4 numeric matrix
Psub = subs(P,P,m);

Note that the output of the subs function is still a symbolic matrix, even if it contains only numbers. To convert a symbolic matrix (or other symbolic variable) to a numeric one, use eval:

Psubnum = eval(Psub);