Voltage and current transformation matrices

Transformation matrices relating two adequate systems of simple network co-ordinates such as node-pair voltages or link currents belong to the class of unimodular or E-matrices. The paper makes a distinction between the matrices corresponding to such voltage and current transformations, and different sets of necessary conditions are derived for each type. Since the loop- and cut-set-to-branch incidence matrices are closely related to transformation matrices, the discussion proposes new sets of necessary conditions for incidence matrices corresponding to systems of node-pair voltages or link currents. Examples are given of matrices which whilst representing a voltage transformation cannot represent a current transformation and vice versa. Another example shows an E-matrix which can represent neither a voltage nor a current transformation.