International Journal of Statistics and Applied Mathematics
  • Printed Journal
  • Indexed Journal
  • Refereed Journal
  • Peer Reviewed Journal

2022, Vol. 7, Issue 4, Part C

Structure of decomposable semigroups of nonnegative r-Potent matrices in Mn (R)


Author(s): Alka Marwaha and Rashmi Sehgal Thukral

Abstract: An r-potent matrix [9] in Mn (R) is an n×n matrix satisfying Er=E. An idempotent matrix is an r-potent with r=2. A multiplicative semigroup S in Mn (R) is to be said decomposable (see [2]) if there exists a special kind of common invariant subspace called standard invariant subspace for each A∈S. A semi-group S of non-negative r-potent matrices in Mn (R) is known (see [5]) to be decomposable if rank (S)>r-1 for all S in S. Our contributions in this paper are as follows: We study the structure of decomposable semi-groups of non-negative r-potent matrices in Mn (R). We reduce these decomposable semi-groups into standard block triangular form wherein the diagonal blocks form constant rank indecomposable semi-groups of non-negative r-potents. Under the special condition of fullness, we obtain a block diagonalization of the decomposable semigroup of non-negative r-potent matrices. Lastly, we shall illustrate the complete structure of the maximal indecomposable semigroup of 2-potents (idempotent) with constant rank one.

Pages: 215-225 | Views: 278 | Downloads: 18

Download Full Article: Click Here
How to cite this article:
Alka Marwaha, Rashmi Sehgal Thukral. Structure of decomposable semigroups of nonnegative r-Potent matrices in Mn (R). Int J Stat Appl Math 2022;7(4):215-225.
International Journal of Statistics and Applied Mathematics

International Journal of Statistics and Applied Mathematics


Call for book chapter
International Journal of Statistics and Applied Mathematics