Dimension of N-ports

The recently introduced concept of the dimension of an algebraicnport [1] is shown to be an invariant of thenport. 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. andwis annvector, (Unless specified otherwise, all vectors are column vectors. A vectorx ∈ Rⁿis written asx- = [x₁,x₂,⋯,Xₙ,]. Whenxis the composite of two vectorsy ∈ Rᵏandz ∈ Rⁿ⁻ᵏ, we writex = [y,z]. In addition, we let 0 denote zero matrices of appropriate dimensions and1ₖ, denote the identity matrix of orderk.) is not the most general form for characterizing a linearnport. A generalization of (1) which covers all linear algebraicnports is presented.