The Cayley-Hamilton theorem for noncommutative semirings

Authors:
Radu Grosu
Affiliations:
Department of Computer Science, Stony Brook University, Stony Brook, NY
Venue:
CIAA'10 Proceedings of the 15th international conference on Implementation and application of automata
Year:
2010

Citing 5
Cited 0

The algorithmic analysis of hybrid systems

Theoretical Computer Science - Special issue on hybrid systems
A unified approach to global program optimization

POPL '73 Proceedings of the 1st annual ACM SIGACT-SIGPLAN symposium on Principles of programming languages
Numerical Recipes in C: The Art of Scientific Computing

Numerical Recipes in C: The Art of Scientific Computing
Hybrid I/O automata

Information and Computation
Finite Automata as Time-Inv Linear Systems Observability, Reachability and More

HSCC '09 Proceedings of the 12th International Conference on Hybrid Systems: Computation and Control

Quantified Score

Hi-index	0.00

Visualization

Abstract

The Cayley-Hamilton theorem (CHT) is a classic result in linear algebra over fields which states that a matrix satisfies its own characteristic polynomial. CHT has been extended from fields to commutative semirings by Rutherford in 1964. However, to the best of our knowledge, no result is known for noncommutative semirings. This is a serious limitation, as the class of regular languages, with finite automata as their recognizers, is a noncommutative idempotent semiring. In this paper we extend the CHT to noncommutative semirings. We also provide a simpler version of CHT for noncommutative idempotent semirings.