In this paper

a method based on the triangular unequality is used to explain themaximum power transfer theorem in n-ports network. This method of proof is not only rigid and terse

it can also determine directly the condition of the maximum power transfer and the supremum of the available power drawn by the terminated load. Moreover

with this method

it is not necessary to decide whether the extreme value is of local or global optimum nor is it necessary to determine whether the objective function is convex or non-convex prior to finding the extreme value. However

these are unavoidable requirements if the usual varia-tional method is employed.The general formula of the optimum load impedance is derived in a detailed manner when internal impedance of network

Hermite matrix Zs+Zs*

is positive definite. It would appear that there are infinite numbers of the optimal load impedance matrices satisfying the maximum power transfer condition

where all solutions except one are nontrivial. The set composed of all these solutions constitutes a n2-n dimensional linear submanifold in complex space Cn2 . It is to be noted that trivial solution may evade influence of source vectors

and as is well known

this is an important characteristic in its implementation

but it requires to achieve match between corresponding components of the mutual impedance respectively. In contrast

those nontrivial solution may avoid such a difficult task of matching between corresponding components of the mutual impedance

but the influence of source vectors cannot be avoided.This paper applies

some mathematical accomplishments based on intuitive conception of projective geometry and the theory of generalized inverses

which are good at dealing with the problem considered impossible to solve in the sense of a solution of a nonsingular problem

i. e. the so-called "ill-posed" linear problem. Obviously

the optimal current will be solved if internal impedance of network Zs+Zs* is positive semidefinite. Hence

the optimal load impedance matrices may be found provided that results obtained in the positive definite condition are utilized directly. Finally

it also shows by the operation of cardinal numbers that the numbers of optimal load impedances make no difference between the positive definite and positive semidefinite conditions.