Applications of theory of simultaneous diagonalization of several Hermitian forms †

Abstract

In this paper sets of necessary and sufficient conditions for simultaneous reducibility to diagonal forms of two or more prescribed Hermitian forms are summarized and the procedure for computation of the required transformation outlined, with a view towards applying these results in various problems of electronics. Application of the results to Foster-type canonic synthesis of networks containing positive and negative resistors, inductors and capacitors is discussed. The theory is also applied towards a solution of a certain problem occurring in the Anderson-Duffin parallel addition of matrices. Furthermore, other possible applications are discussed, and examples included, wherever these serve to illustrate better the procedure.