  The $G^{+}$ method is a new method, a powerful one, for the study of
(homogeneous and nonhomogeneous) products of nonnegative matrices -- for
problems on the products of nonnegative matrices. To study such products, new
classes of matrices are introduced: that of the sum-positive matrices, that of
the $\left[ \Delta \right] $-positive matrices on partitions (of the column
index sets), that of the $g_{k}^{+}$-matrices... On the other hand, the
$g_{k}^{+}$-matrices lead to necessary and sufficient conditions for the
$k$-connected graphs. Using the $G^{+}$ method, we prove old and new results
(Wielandt Theorem and a generalization of it, etc.) on the products of
nonnegative matrices -- mainly, sum-positive, $\left[ \Delta \right] $-positive
on partitions, irreducible, primitive, reducible, fully indecomposable,
scrambling, or Sarymsakov matrices, in some cases the matrices being, moreover,
$g_{k}^{+}$-matrices (not only irreducible).
