In part 1, we propose a statistical technique to
the solution of stationary eigenvectors of Markov chains
that is more efficient and more precise than the classical
algebraic method. However, it only fails when the
Markov matrix is not invertible, which is also the case
for the classical solution. In part 2, we propose an
important principle valid for B-Matrix chains: [For a
positive symmetric physical matrix, the sum of their
eigenvalues powers is equal to the eigenvalue of their
sum of the series of powers of the matrix]. This principle
is validated numerically by the derivation of an
important equation for the sum of the series of algebraic
powers, namely
