
Accession Number : AD0770707
Title : Bounded Groups and NormHermitian 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 NormHermitian Matrices.Technical summary rept.,Deutsch,Emeric ;Schneider,Hans ;MRCTSR1349DA31124ARO(D)462, NSFGP37978*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 nspace, it follows that there exists a nonsingular n x n matrix L (the LoewnerJohn matrix for the norm) such that LH(L sup (1)) is Hermitian for every normHermitian 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