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Askar Ali M

Publications and source records attributed to Askar Ali M.

7 recordsLinked to original sources
arXiv2026

On matrix polynomials and the joint spectral radius over max-algebras

Our aim is to study matrix polynomials over max-algebras and their growth in terms of max-induced seminorms. In particular, we compare the set growth of a bounded family $Ψ$ of matrix polynomials, measured in terms of the seminorms $η_{\|\cdot\|}$ and $\hatη_{\|\cdot\|}$ with the induced joint spectral radius of the coefficient pool $Ψ_0$ of the matrix polynomials. Dynamics of max-linear maps and convergence to periodic points under a single joint spectral radius condition and the existence of common max-eigenvectors of the coefficient pool are also brought out.

math.RA↗
arXiv2026

Simultaneous triangularization over max-algebras

The purpose of this article is to investigate triangularization and simultaneous triangularization of matrices over max algebras using graph theoretic methods. We establish a connection between commutators and commutants with simultaneous triangularization over max algebras. We also define the notion of characteristic polynomial of a collection in terms of the tropical determinant and determine when it can be written as a product of linear terms. Algorithms for all of the above are also brought out.

math.RA↗
arXiv2024

A Canonical Form for Max Plus Symmetric Matrices and Applications

We develop a canonical form for congruence of max plus symmetric matrices. We use the same canonical form to get results in the generalized eigenvector problem. We have also utilized the canonical form to find all symmetric matrices that commute with a given symmetric matrix.

math.RA↗
arXiv2024

Tropical Matrix Exponential

In this article, we introduce an exponential for tropical matrices and show that this series is essential for the analysis of certain kinds of stability in discrete event dynamic systems. A notion of a generalised eigenvector is introduced to discuss this kind of stability and prove it exists at most in the order of $1,p/2,p$, where $p$ is the period of the corresponding matrix. Thus characterizing the generalised eigenvectors of all powers of the matrix. Also, a sufficient condition is proved for the exponential of a matrix to be robust.

math.RA↗
arXiv2024

Solutions to a system of Yang-Baxter matrix equations

In this article, a system of Yang-Baxter-type matrix equations is studied, $XAX=BXB$, $XBX=AXA$, which "generalizes" the matrix Yang-Baxter equation and exhibits a broken symmetry. We investigate the solutions of this system from various geometric and topological points of view. We analyze the existence of doubly stochastic solutions and intertwining solutions to the system and describe the conditions for their existence. Furthermore, we characterize the case when $A$ and $B$ are idempotent orthogonal complements. i.e., $A^2 =A, B^2= B, AB = BA =0$. We also completely characterize the set of solutions for $n=2$ using commutative algebraic techniques.

math.RA↗
arXiv2023

Solutions to the matrix Yang-Baxter equation

In this article, we give a few classes of solutions for the Yang-Baxter type matrix equation, $AXA=XAX$. We provide all solutions for the cases when $A$ is equivalent to a Jordan block or has precisely two Jordan blocks. We also have given a few general properties of the solutions of the YB-equation.

math.RA↗