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.

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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

Section

Research Article