Abstracts

Simultaneous triangularization over max-algebras

Sachindranath Jayaraman ,  IISER Thiruvananthapuram

By a max-algebra, we mean the triple $(\mathbb{R}_{+}, \oplus, \otimes)$, where $\mathbb{R}_{+}$ denotes the set of nonnegative real numbers, $\oplus$ denotes the binary operation of taking the maximum of two nonnegative numbers and $\otimes$ is the usual multiplication of two numbers. The purpose of this presentation is to bring out some results on simultaneous triangularization of a pair $(A,B)$ of matrices over max-algebras in terms of acyclicity of the associated digraph. We point out connections between commutators and commutants with simultaneous triangularization over max-algebras. We also define the characteristic polynomial of the pair $(A,B)$ in terms of the tropical determinant, point out its connection with simultaneous triangularization and determine when it can be written as a product of linear terms. This talk is based on the joint work \href{https://arxiv.org/abs/2510.07855}{arXiv:2510.07855} with Askar Ali M. and Himadri Mukherjee.