If X=[x1,x2,...,xn]' where x1+x2+...+xn=1.

If A1,A2,...,An are nXn square matrices, all elements are greater than 0 and less than 1.

The sum of all elements of A1 is n. It is also true for A2,...,An.

A1+A2+...+An=E, where E is a matrix of all 1s.

Now we update X by doing followings:

x1(t+1)=X(t)'*A1*X(t)

x2(t+1)=X(t)'*A2*X(t)

...

xn(t+1)=X(t)'*An*X(t)

when t->infinite, what is X?

Thanks.