Some maximal absolutely unstable sign patterns of 4×4 matrices

✍ Scribed by Juichi Miyamichi

• Book ID: 104300877
• Publisher: Elsevier Science
• Year: 1982
• Tongue: English
• Weight: 339 KB
• Volume: 1
• Category: Article
• ISSN: 0167-6911
• DOI: 10.1016/s0167-6911(82)80055-8

✦ Synopsis

In this paper we discuss the absolute instability of the 4X4 qualitative matrices whose diagonal elements are 0, 0, °and -.

A matrix is said to be stable if all its characteristic values have negative real parts. A sign pattern (+. -.0) of a matrix is said to be absolutely unstable if there is no stable matrix which has the sigri pattern. Of 531441 different patterns. 299953 arc found to be absolutely unstable. By using thc overpallern-subpattern concept we can define an order relation in the set of qualitative matrices and it is found that there are 12 basic absolutely unstable sign patterns which are maximal.