DID YOU KNOW? DTIC has over 3.5 million final reports on DoD funded research, development, test, and evaluation activities available to our registered users. Click

HERE to register or log in.

# Accession Number:

## AD0770707

# Title:

## Bounded Groups and Norm-Hermitian Matrices.

# Descriptive Note:

## Technical summary rept.,

# Corporate Author:

## WISCONSIN UNIV MADISON MATHEMATICS RESEARCH CENTER

# Report Date:

## 1973-10-01

# Pagination or Media Count:

##
34.0

# Abstract:

## MATHEMATICS RESEARCH CENTERBounded Groups and Norm-Hermitian Matrices.Technical summary rept.,Deutsch,Emeric Schneider,Hans MRC-TSR-1349DA-31-124-AROD-462, NSF-GP-37978GroupsMathematics, MatricesMathematics, 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 LHL sup -1 is Hermitian for every norm-Hermitian H. Numerous applications of this result are given. Author

# Distribution Statement:

## APPROVED FOR PUBLIC RELEASE

#