Further Matrix Classes Possessing the Interval Property

Abstract

In this article, the collection of classes of matrices which possess the interval property presented in [J. Garloff, M. Adm, and J. Titi, A survey of classes of matrices possessing the interval property and related properties, Reliab. Comput., 22:1-14, 2016] is continued. That is, given an interval of matrices with respect to a certain partial order, it is desired to know whether a special property of the entire matrix interval can be inferred from some of its elements lying on the vertices of the matrix interval. The interval property of some matrix classes found in the literature is presented, and the interval property of further matrix classes including the ultrametric, the conditionally positive semidefinite, and the infinitely divisible matrices is given for the first time. For the inverse M-matrices, the cardinality of the required set of vertex matrices known so far is significantly reduced.