The Primitivity and Primitive Exponents of a Class of Nonnegative Matrix Pairs

DOI

10.2991/emim-17.2017.32How to use a DOI?

Keywords

Upper bound; Nonnegative; Matrix pairs; Two-Colored digraph; Exponent

Abstract

It is a brand-new research in combinatorial matrix theory to extend the exponent of traditional single nonnegative primitive matrix to the exponent of nonnegative primitive matrix pairs. With the knowledge of graph theory, the problem of primitive exponent of nonnegative matrix pairs can be transformed into the associated directed digraph of nonnegative matrix pairs, that is two-colored digraphs. A class of two-colored digraphs whose uncolored digraph has vertices and consists of one -cycle and one -cycle is considered. The primitive conditions, the upper bound, the lower bound, and the characterizations of extremal two-colored digraphs are given. The results provide a basis for the study of the exponent of nonnegative primitive matrix pairs and the exponent of nonnegative primitive matrix tuples in the general case.

Copyright

© 2017, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - CONF
AU  - Meijin Luo
PY  - 2017/04
DA  - 2017/04
TI  - The Primitivity and Primitive Exponents of a Class of Nonnegative Matrix Pairs
BT  - Proceedings of the 7th International Conference on Education, Management, Information and Mechanical Engineering (EMIM 2017)
PB  - Atlantis Press
SP  - 148
EP  - 151
SN  - 2352-538X
UR  - https://doi.org/10.2991/emim-17.2017.32
DO  - 10.2991/emim-17.2017.32
ID  - Luo2017/04
ER  -