Some Properties of Matrices with 1, -1 and 0 Entries

✍ Scribed by Reza Hashemian

• Publisher: Elsevier Science
• Year: 1973
• Tongue: English
• Weight: 700 KB
• Volume: 295
• Category: Article
• ISSN: 0016-0032
• DOI: 10.1016/0016-0032(73)90206-8

✦ Synopsis

A class of matrices with 1, -1 and 0 entrim, called the H-matrices, i8 introduced and properties of such matrices are investigated. It k shown that for an H-matrix K the matrix B = KDKT, where D is a diagonal matrix with nonnegative diagonal entries, ha8 certain properties applicable to topological synthesis of networks. A technique for decomposing a particular symmetrical matrix G, called the Q-matrix, into KDKT, where K is an H-matrix and D is a diagonal matrix with po&ve diagonal entriea, is also developed.

* In general, two matrices K, and K, are assumed identical, for the purposes of our discussion, provided that K, is obtained from K, after permuting some rows and columns of K1 and/or multiplying some rows and columns of K, by -1.