Dominant matrices and max algebra

Nonnegative matrices, max-algebra and applications

Ela Applications of Max Algebra to Diagonal Scaling of Matrices

Results are proven on an inequality in max algebra and applied to theorems on the diagonal similarity scaling of matrices. Thus the set of all solutions to several scaling problems is obtained. Also introduced is the “full term rank” scaling of a matrix to a matrix with prescribed row and column maxima with the additional requirement that all the maxima are attained at entries each from a diffe...

Eigenvectors of interval matrices over max-plus algebra

The behaviour of a discrete event dynamic system is often conveniently described using a matrix algebra with operations max and plus Such a system moves forward in regular steps of length equal to the eigenvalue of the system matrix if it is set to operation at time instants corresponding to one of its eigenvectors However due to imprecise measurements it is often unappropriate to use exact mat...

Products of irreducible random matrices in the (Max,+) Algebra

We consider the recursive equation “x(n + 1) = A(n) ⊗ x(n)” where x(n + 1) and x(n) are Rk-valued vectors and A(n) is an irreducible random matrix of size k × k. The matrix-vector multiplication in the (max,+) algebra is defined by (A(n) ⊗ x(n))i = maxj(Aij(n) + xj(n)). This type of equation can be used to represent the evolution of Stochastic Event Graphs which include cyclic Jackson Networks,...

On Semigroups of Matrices in the (max,+) Algebra

We show that the answer to the Burnside problem is positive for semigroups of matrices with entries in the (max;+)-algebra (that is, the semiring (R[ f 1g;max;+)), and also for semigroups of (max;+)-linear projective maps with rational entries. An application to the estimation of the Lyapunov exponent of certain products of random matrices is also discussed. Key-words: Semigroups, Burnside Prob...