Dominant matrices and their application to network synthesis under topological constraints

✍ Scribed by I. Cederbaum

• Publisher: Elsevier Science
• Year: 1964
• Tongue: English
• Weight: 885 KB
• Volume: 278
• Category: Article
• ISSN: 0016-0032
• DOI: 10.1016/0016-0032(64)90091-2

✦ Synopsis

In this paper some algebraic properties of the Gaussian decomposition of a dominant 1 matrix into a product of a lower and an upper triangular matrix, are discussed. It is shown that many properties of the parent dominant matrix are preseTved in the derived triangular matrices. Moreover, around any such decomposition, A = T'T, with A-dominant and T-upper triangular, a family of dominant matrices, T'DT, may be defined. It is shown in the paper, that this method of generating new dominant matrices, proves to be of importance in the theory of elecf,rical networks. The paper contains some examples of the application of this concept to synthesis of two-element-kind network functions if the realization is constrained to be achieved around a given one-element-kind subnetwork.