Canonic forms of Brune and Darlington 2n-ports

The Brune and Darlington syntheses for one-ports have been extended to n-ports by several authors. the synthesis algorithms are well established and are not discussed in this paper, which is essentially concerned with the minimal realizations (in the total number of elements, including ideal transformers) of the 2n-ports occurring as building-blocks in the synthesis. A unified view of that subject is presented, including many new results and a critical survey of the literature. an appendix dealing with the contragradient reduction of a pair of rectangular matrices is of independent algebraic interest.