Accession Number : AD0770707

Title :   Bounded Groups and Norm-Hermitian Matrices.

Descriptive Note : Technical summary rept.,

Corporate Author : WISCONSIN UNIV MADISON MATHEMATICS RESEARCH CENTER

Personal Author(s) : Deutsch,Emeric ; Schneider,Hans

Report Date : OCT 1973

Pagination or Media Count : 34

Abstract : MATHEMATICS RESEARCH CENTERBounded Groups and Norm-Hermitian Matrices.Technical summary rept.,Deutsch,Emeric ;Schneider,Hans ;MRC-TSR-1349DA-31-124-ARO(D)-462, NSF-GP-37978*Groups(Mathematics), *Matrices(Mathematics), TheoremsHermitian matricesAn elementary proof is given that a bounded multiplicative group of n x n complex (real) nonsingular matrices is similar to a unitary (orthogonal) group. Given a norm on complex n-space, it follows that there exists a nonsingular n x n matrix L (the Loewner-John matrix for the norm) such that LH(L sup (-1)) is Hermitian for every norm-Hermitian H. Numerous applications of this result are given. (Author)

Descriptors :   *GROUPS(MATHEMATICS), *MATRICES(MATHEMATICS), THEOREMS

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE