EP-nilpotent decomposition and its applications

ABSTRACT

In this paper, we introduce the notion of the EP-nilpotent decomposition and present some of its applications. By applying the decomposition, we introduce two partial orders (the E-N partial order and the E-S partial order) and characterize their properties. The two partial orders above are non-minus-type partial orders, although the method used to introduce the two partial orders is similar to that of the C-N partial order, a minus-type partial order.

KEYWORDS:

• Matrix decomposition
• EP-nilpotent decomposition
• EP matrix
• nilpotent matrix
• E-N partial order
• E-S partial order

2010 MSC:

• 15A09
• 15A57
• 15A24

Acknowledgments

The authors wish to extend their sincere gratitude to the referees for their precious comments and suggestions.

Disclosure statement

No potential conflict of interest was reported by the authors.

Correction Statement

This article has been republished with minor changes. These changes do not impact the academic content of the article.

Additional information

Funding

The first author was supported by Guangxi Natural Science Foundation [grant 2018GXNSFAA138181], the National Natural Science Foundation of China [grant 11401243, 61772006] and the Special Fund for Bagui Scholars of Guangxi [grant 2016A17]. The second author was supported byGuangxiNatural Science Foundation [grant 2018JJD110003], theNationalNatural Science Foundation of China [grant 11361009], the Special Fund for Science and Technological Bases and Talents of Guangxi [grant 2016AD05050] and High level innovation teams and distinguished scholars in Guangxi Universities.