Decomposability of Nonnegative r-Potent Matrices
Rashmi Sehgal Thukral, Alka Marwaha
TL;DR
This paper investigates the conditions under which nonnegative r-potent matrices are decomposable, providing a structural characterization and extending the results to semigroups of such matrices.
Contribution
It offers a precise characterization of decomposability for nonnegative r-potent matrices and explores their structural properties and semigroup decomposability.
Findings
Derived necessary and sufficient conditions for decomposability.
Established a general structure for r-potent matrices.
Proved that semigroups of r-potent matrices are decomposable.
Abstract
We consider nonnegative r-potent matrices with finite dimensions and study their decomposability. We derive the precise conditions under which an r-potent matrix is decomposable. We further determine a general structure for the r-potent matrices based on their decomposability. Finally, we establish that semigroups of r-potent matrices are also decomposable.
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