A moore-penrose inverse for boolean relation matrices

Abstract

Several authors in recent years investigated the properties of the Moore-Penrose inverse of an arbitrary Boolean relation matrix. The concept of a Moore-Penrose inverse for Boolean relation matrices was discussed first by Rutherford [11] and then independently discovered by Markowsky [8], Plemmons [10], and the author ([3] and [4]). It is natural to inquire whether or not the Moore-Penrose inverse is unique, if it exists. In this paper, the properties of unique Moore-Penrose inverse of an arbitrary Boolean relation matrix are examined in connection with partial order relation and three computational methods for the unique Moore-Penrose inverse for an arbitrary Boolean relation matrix is developed.KeywordsGeneralize InversePartial Order RelationNonsingular MatriceBoolean MatricePenrose InverseThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.