ANALYSIS OF ACTIVE NETWORKS BY TOPOLOGICAL EXPANSION OF DETERMINANTS

In a recent paper, it was suggested to evaluate the determinant of an (active) network, in reduced form, partly from the trees of a network, by using a topological expansion of a determinant. The present paper investigates this method and compares it with other methods. The determinant expansion rule is proved and generalized. Then some similar expansion rules are derived. An example is analyzed by various methods, showing that the proposed expansion produces the reduced determinant, while with unistor concepts some redundant terms are obtained. The advantages and drawbacks of the method are discussed along with its relationship to other methods.