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 ;MRC-TSR-1379DA-31-124-ARO(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 Stein-Pfeffer 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