Realization of fourth-order singular and quasi-singular resistance and conductance matrices

A new result in resistance network synthesis is proved, namely, that any fourth-order singular and quasi-singular matrix is realizable as a resistance and a conductance matrix if and only if it is paramount. Indefinite and quasi-indefinite matrices are treated first, followed by nonindefinite singular and quasi-singular matrices. Canonic networks and element-value formulas are given for all cases. In addition, it is pointed out that the new result includes the fourth-order solution to an open problem stated by Nambiar.