Generalized inverses of Boolean tensors via the Einstein product

Abstract

Applications of the theory and computations of Boolean matrices are of fundamental importance to study a variety of discrete structural models. But the increasing ability of data collection systems to store huge volumes of multidimensional data, the Boolean matrix representation of data analysis is not enough to represent all the information content of the multiway data in different fields. From this perspective, it is appropriate to develop an infrastructure that supports reasoning about the theory and computations. In this paper, we discuss the generalized inverses of the Boolean tensors with the Einstein product. Further, we elaborate on this theory by producing a few characterizations of different generalized inverses and several equivalence results on Boolean tensors. We explore the space decomposition of the Boolean tensors and present reflexive generalized inverses through it. In addition to this, we address rank and the weight for the Boolean tensor.

Keywords:

• Boolean tensor
• generalized inverses
• Moore–Penrose inverse
• Space decomposition
• Boolean rank

AMS subject classifications:

• 15A69
• 15A09

Acknowledgments

The authors would like to thank the handling editor and referees for their detailed comments and suggestions.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This research work was supported by Science and Engineering Research Board (SERB), Department of Science and Technology, India [grant number EEQ/2017/000747].