arXiv subjects

S. M. Manjegani

Publications and source records attributed to S. M. Manjegani.

3 recordsLinked to original sources

arXiv2026

Calculating eigenvectors in max-algebra by mutation-sunflower method

In this article we introduce a new method, which we call a mutation-sunflower method, for calculating max-eigenvectors of a nonnegative irreducible $n\times n$ matrix $A$. Our method works in the general irreducible case, but it is in comparison with existing methods most effective for some special classes of matrices for example for sparse enough matrices. Our method reduces to solving max-eigenproblems for simple mutation-sunflower matrices that have exactly one positive entry in each row. We include some instructive examples.

math.CO↗

arXiv2025

Stochastic matrices and majorization in max algebra

In this paper, we introduce and characterize max-doubly stochastic matrices within the framework of max algebra, where the operations are defined as $x \oplus y = \max(x, y)$ and $x \otimes y = xy$. We explore the fundamental properties of max-doubly stochastic matrices and their role in vector majorization. Specifically, we establish that for vectors $x$ and $y$ in max algebra, $x$ is majorized by $y$ if there exists a max-doubly stochastic matrix $D$ such that $x = D \otimes y$. This provides a new approach to majorization theory within tropical mathematics and enhances the understanding of vector relations in max algebra.

math.RA↗

arXiv2021

Asymptotic formulae and inequalities for point spectrum in max algebra

We prove new explicit asymptotic formulae between (geometric) eigenvalues in max-algebra and classical distinguished eigenvalues of nonnegative matrices, which are useful tools for transferring results between both settings. We establish new inequalities for both types of eigenvalues of Hadamard products and Hadamard weighted geometric means of nonnegative matrices. Moreover, a version of the spectral mapping theorem for the distinguished spectrum is pointed out.

math.FA↗