Bounded groups and norm-Hermitian matrices

Abstract

An elementary proof is given that a bounded multiplicative group of complex (real) n×n nonsingular matrices is similar to a unitary (orthogonal) group. Given a norm on a complex n-space, it follows that there exists a nonsingular n×n matrix L (the Loewner-John matrix for the norm) such that LHL-1 is Hermitian for every norm-Hermitian H. Numerous applications of this result are given. © 1974.