Stable matrices, the Cayley transform, and convergent matrices

Autor: Tyler Haynes
Jazyk: angličtina
Rok vydání: 1991
Předmět:
Zdroj: International Journal of Mathematics and Mathematical Sciences, Vol 14, Iss 1, Pp 77-81 (1991)
Druh dokumentu: article
ISSN: 0161-1712
1687-0425
01611712
DOI: 10.1155/S0161171291000078
Popis: The main result is that a square matrix D is convergent (limn→∞Dn=0) if and only if it is the Cayley transform CA=(I−A)−1(I+A) of a stable matrix A, where a stable matrix is one whose characteristic values all have negative real parts. In passing, the concept of Cayley transform is generalized, and the generalized version is shown closely related to the equation AG+GB=D. This gives rise to a characterization of the non-singularity of the mapping X→AX+XB. As consequences are derived several characterizations of stability (closely related to Lyapunov's result) which involve Cayley transforms.
Databáze: Directory of Open Access Journals
Externí odkaz: