Inverses of Infinite Sign Regular Matrices

摘要

Let A be an infinite sign regular (SR) matrix which can be viewed as a bounded linear operator from L sub infinity to itself. It is proved here that if the range of A contains the sequence (...,1,-1,1,-1,...), then A is onto. If (inverse of A) exists then D (inverse of A) D is also SR, where D is the diagonal matrix with diagonal entries alternately 1 and -1. In case A is totally positive (TP), then D (inverse of A) D is also TP under additional assumptions on A. (Author)