Properties of Hadamard product of inverse M ‐matrices
Chuansheng Yang, Chengxian Xu · Numerical Linear Algebra with Applications · 2004
Abstract This paper concerns with the properties of Hadamard product of inverse M ‐matrices. Structures of tridiagonal inverse M ‐matrices and Hessenberg inverse M ‐matrices are analysed. It is proved that the product A ○ A T satisfies Willoughby's necessary conditions for being an inverse M ‐matrix when A is an irreducible inverse M ‐matrix. It is also proved that when A is either a Hessenberg inverse M ‐matrix or a tridiagonal inverse M ‐matrix then A ○ A T is an inverse M ‐matrix. Based on these results, the conjecture that A ○ A T is an inverse M ‐matrix when A is an inverse M ‐matrix is made. Unfortunately, the conjecture is not true. Copyright © 2004 John Wiley Sons, Ltd.