Finiteness of the Cyclic Group Related to the Group Inverse of A Matrix and Finite Markov Chains

Authors

  • Hanifa Zekraoui Faculty of Exacts and natural Sciences, University of L'arbi-Ben-M'hidi, Oum-El-Bouaghi

DOI:

https://doi.org/10.26713/cma.v4i1.158

Keywords:

Generalized inverse, Group inverse, Finite cyclic group, Markov chains

Abstract

The Group inverse is one of the generalized inverses possessing the properties the closest to the normal inverse. The positive and negative powers of a given matrix $A$ (the latter being interpreted as powers of $A^{\#}$, the group inverse of $A$), together with the projector $AA^{\#}$ as the unit element, constitute an Abelian group. In this paper, we are going to give equivalent conditions so that this group is finite, and applying the result in finite Markov chains.

Downloads

Download data is not yet available.

Downloads

CITATION

How to Cite

Zekraoui, H. (2013). Finiteness of the Cyclic Group Related to the Group Inverse of A Matrix and Finite Markov Chains. Communications in Mathematics and Applications, 4(1), 15–20. https://doi.org/10.26713/cma.v4i1.158

Issue

Vol. 4 No. 1 (2013)

Section

Research Article

License

Creative Commons Licence 4.0 by  

Authors who publish with this journal agree to the following terms:

  • Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a CCAL that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
  • Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
  • Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work.