3 papers
math.CO2026
Properties of the Tropical Characteristic Polynomial of Symmetric Matrices
Dariush Kiani, Hanieh Tavakolipour
We investigate the combinatorial structure of the tropical characteristic polynomial of symmetric matrices using the tropical permanents of their principal submatrices. We establis…
math.RA2026
Generalized Eigenvectors and Rayleigh bounds for tropical algebraic eigenvalues
Dariush Kiani, Hanieh Tavakolipour
In this paper, we review the eigenpair problem in the context of tropical algebra. An important fact that has been largely overlooked in spectral theory of tropical algebra is that…
math.RA2025
Spectral Properties of Positive Definite Matrices over Symmetrized Tropical Algebras and Valued Ordered fields
Marianne Akian, Stephane Gaubert, Dariush Kiani +1
We investigate the properties of positive definite and positive semi-definite symmetric matrices within the framework of symmetrized tropical algebra, an extension of tropical alge…