The product matrices and new gain formulas

New matrices, the product matrix
P
, the voltage product matrix
p^{\upsilon}
, and the current product matrix
P^i
, are defined at first. And new gain formulas
T^{\upsilon}_{qp}
for the voltage gain and
T^{i}_{qp}
, for the current gain are presented on the basis of the product matrices. Although the formulas are topological ones, the procedures for their evaluations are quite systematic, completely indirect and purely numerical, and no sign rule is required. So the new formulas are suitable for computer-aided symbolic network analysis without restriction on symbols, in number or type.