Dimension of N-ports

The recently introduced concept of the dimension of an algebraic
n
port [1] is shown to be an invariant of the
n
port. This property led to a unique classification of all linear algebraic n ports in terms of their dimensions. Contrary to common belief, it is shown that the representation port-current vectors. and
w
is an
n
vector, (Unless specified otherwise, all vectors are column vectors. A vector
x \in R^{n}
is written as
x- = [x_{1},x_{2},\cdots,X_{n},]
. When
x
is the composite of two vectors
y \in R^{k}
and
z \in R^{n-k}
, we write
x = [y,z]
. In addition, we let 0 denote zero matrices of appropriate dimensions and
1_{k}
, denote the identity matrix of order
k
.) is not the most general form for characterizing a linear
n
port. A generalization of (1) which covers all linear algebraic
n
ports is presented.