Invertible matrices over finite additively idempotent semirings
Andreas Kendziorra, Stefan E. Schmidt, Jens Zumbr\"agel
TL;DR
This paper studies invertible matrices over finite additively idempotent semirings, providing criteria for invertibility, methods to construct inverses, and formulas to count such matrices.
Contribution
It introduces a criterion for invertibility, a construction method for inverse matrices, and a formula for counting invertible matrices over these semirings.
Findings
Established a criterion for invertibility of matrices
Provided a construction method for inverse matrices
Derived a formula for counting invertible matrices
Abstract
We investigate invertible matrices over finite additively idempotent semirings. The main result provides a criterion for the invertibility of such matrices. We also give a construction of the inverse matrix and a formula for the number of invertible matrices.
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Taxonomy
Topicssemigroups and automata theory · Rings, Modules, and Algebras · Advanced Algebra and Logic