Accession Number : AD0771390

Title :   On Ranges of Lyapunov Transformations. III.

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 : 35

Abstract : Technical summary rept.,SLoewy,Raphael ;MRC-TSR-1385DA-31-124-ARO(D)-462*Matrices(Mathematics), *Transformations(Mathematics), Eigenvectors, TheoremsHermitian matrices, Lyapunov functionsThe Lyapunov transformation (L sub A) corresponding to the matrix A element of (c sup n,n) is a linear transformation on the space (H sub n) of hermitian matrices H element of (c sup n,n) of the form (L sub A)(H) = AH + HA*. Let (C sub 1)(A) = (AH + HA*: H is hermitian and positive semidefinite). Given A element of (c sup n,n such that (L sub A) is invertible, the author characterizes the matrices b element of (c sup n,n) such that (C sub 1)(A) = (C sub 1)(B).

Descriptors :   *MATRICES(MATHEMATICS), *TRANSFORMATIONS(MATHEMATICS), EIGENVECTORS, THEOREMS

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE