On the asymptotic stability of nonnegative matrices in max algebra

Nonnegative matrices, max-algebra and applications

On Commuting Matrices in Max Algebra and in Classical Nonnegative Algebra

This paper studies commuting matrices in max algebra and nonnegative linear algebra. Our starting point is the existence of a common eigenvector, which directly leads to max analogues of some classical results for complex matrices. We also investigate Frobenius normal forms of commuting matrices, particularly when the Perron roots of the components are distinct. For the case of max algebra, we ...

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...

On the nonnegative inverse eigenvalue problem of traditional matrices

In this paper, at first for a given set of real or complex numbers $sigma$ with nonnegative summation, we introduce some special conditions that with them there is no nonnegative tridiagonal matrix in which $sigma$ is its spectrum. In continue we present some conditions for existence such nonnegative tridiagonal matrices.

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