# 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):

# 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

# Descriptors:

# Subject Categories:

- Theoretical Mathematics