Thread: Matrix equation forming a straight line

Ok I hope this is the right place to post this, I have not been able to find anything about this anywhere. I'm probably missing some simple definition or something.

We have to explain why the plotted vector points v,A.v,...,(A^9).v resulting from the matrix equation form a straight line.

Well it turns out its because both matrix and vector are stochastic. A stochastic matrix multiplied with a stochastic vector will always yield a stochastic vector (this can be shown) so by the rule of A(BC)=(AB)C the result will always have to be stochastic no matter how many times you take the matrix to a power and so the x and y "coordinates" must conform to x+y=1 which means a straight line.

Maybe this can help someone else.