On the sign pattern of network matrices

✍ Scribed by David P. Brown; Myril B. Reed

• Publisher: Elsevier Science
• Year: 1962
• Tongue: English
• Weight: 426 KB
• Volume: 273
• Category: Article
• ISSN: 0016-0032
• DOI: 10.1016/0016-0032(62)91093-1

✦ Synopsis

Any synthesis process based on a node-pair or mesh matrix must take cognizance of the sign pattern of the matrix. It is proved in general terms in this paper that:

(1) the only subgraph of a connected graph G wbich need be of concern in studying the sign pattern of the node-pair (mesh) matrix is the tree (cotree), ( 2) there is a one-toone correspondence between changing the orientation of a branch of any tree of G and a row and column sign change of the corresponding node-pair matrix for diagonal element admittance matrix, and (3) there is a one-to-one correspondence between changing the orientation of an element of any cotree of G and a row and column sign change of the corresponding mesh matrix for diagonal element impedance matrix. This definition is similar to Definition 4 of (3) where the operation of cross-sign charge is defined for symmetrical matrices only. The properties of matrices which follow Definition 1 in this paper hold for nonsymmetrical matrices.