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Properties of Hadamard product of inverse M ‐matrices
Author(s) -
Yang Chuansheng,
Xu Chengxian
Publication year - 2004
Publication title -
numerical linear algebra with applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.02
H-Index - 53
eISSN - 1099-1506
pISSN - 1070-5325
DOI - 10.1002/nla.364
Subject(s) - mathematics , hadamard product , hadamard transform , inverse , product (mathematics) , complex hadamard matrix , hadamard matrix , combinatorics , mathematical analysis , geometry
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.