Given a set of column vectors $v_1, v_2,...,v_t$ is there a way to calculate a unique transition matrix?
In other words, is there one and only one matrix $A$ such that $Av_{i} = v_{i+1}$?
Additionally, is it possible to find the "transition matrix of best fit" for $v_1, v_2,...v_t$? In other words, the matrix $A$ that minimizes the error between a predicted vector and the actual?
I'm asking because I'm trying to use Markov chains to predict a series of column vectors and I'm curious if there's a more "vectorized" (i.e. linear algebra based) implementation of calculating the transition matrix.