Infimum of a matrix norm of A induced by an absolute vector norm

Abstract

We characterize the infimum of a matrix norm of a square matrix A induced by an absolute norm, over the fields of real and complex numbers. Usually this infimum is greater than the spectral radius of A. If A is sign equivalent to a nonnegative matrix B then this infimum is the spectral radius of B.

arXiv comment7 pages, small corrections of previous version