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

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


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


Zbl 0541.00013