Linear algebra in dioids: A survey of recent results. (English) Zbl 0568.08001

Gondran, M.; Minoux, M.

Algebraic and combinatorial methods in operations research, Proc. Workshop, Ann. Discrete Math. 19, 147-164 (1984).

[For the entire collection see Zbl 0541.00013.]
The paper surveys the main results recently obtained in the study of dioids. It is shown that the most important concepts and properties of classical linear algebra such as solution of linear and nonlinear equations, linear dependence and independence, determinants, eigenvalues and eigenvectors may be extended to dioids.

Reviewer: T.Sawik

MSC:

08A02	Relational systems, laws of composition
15A06	Linear equations (linear algebraic aspects)
15A03	Vector spaces, linear dependence, rank, lineability
90B22	Queues and service in operations research
15A15	Determinants, permanents, traces, other special matrix functions

Keywords:

dioids; solution of linear and nonlinear equations; eigenvalues; eigenvectors

Citations:

Zbl 0541.00013