  We found, by Hurwitz's Zeta Function, a new functional equation for Riemann
Zeta Function. Considering this equation for $s=2$ and $s=1$, we determine a
relation between the values of Riemann zeta Function on positive integers. The
Matrix has two dimensions, and the second member is the vector (1,
$-\zeta(2)$). The elements of this vector are linearly independent on the
Rationals; and from this independence, we determined that $\zeta(j)$ is
irrational for each j=3,4,5,6,7,8,9,....

General Mathematics