Bounded Groups and Norm-Hermitian Matrices.
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)
Document Details
- Document Type
- Technical Report
- Publication Date
- Oct 01, 1973
- Accession Number
- AD0770707
Entities
People
- Emeric Deutsch
- Hans Schneider
Organizations
- University of Wisconsin–Madison