2 citations · 2 across the 4 of their papers we have counts for
4 papers
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…
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…
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…
Factorization of polynomials over the symmetrized tropical semiring and Descartes' rule of sign over ordered valued fields
Marianne Akian, Stephane Gaubert, Hanieh Tavakolipour
The symmetrized tropical semiring is an extension of the tropical semifield, initially introduced to solve tropical linear systems using Cramer's rule. It is equivalent to the real…