
Accession Number : AD0771380
Title : On Ranges of Lyapunov Transformations. II.
Descriptive Note : Technical summary rept.,
Corporate Author : WISCONSIN UNIV MADISON MATHEMATICS RESEARCH CENTER
Personal Author(s) : Loewy,Raphael
Report Date : OCT 1973
Pagination or Media Count : 23
Abstract : Y REPT.,SLoewy,Raphael ;MRCTSR1379DA31124ARO(D)462*Matrices(Mathematics), *Transformations(Mathematics), Inequalities, TheoremsLyapunov functions, Hermitian matricesThe Lyapunov transformation (L sub A) corresponding to the matrix A belongs to (c sup n,n) is a linear transformation on the space (H sub n) of hermitian matrices H beongs to (c sup n,n) of the form (L sub A)(H) = AH + HA*. Given a positive stable A belongs to (c sup n,n), the SteinPfeffer Theorem characterizes those K belongs to (H sub n) for which K = (L sub B)(H), where B is similar to A and H is positive definite. Here several extensions of this theorem are proved. (Author)
Descriptors : *MATRICES(MATHEMATICS), *TRANSFORMATIONS(MATHEMATICS), INEQUALITIES, THEOREMS
Subject Categories : Theoretical Mathematics
Distribution Statement : APPROVED FOR PUBLIC RELEASE