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Linear algebra over T-pairs
Marianne Akian, Stephane Gaubert, Louis Rowen
This is part of an ongoing project to find a general algebraic framework for semiring theory. The structure theory of semirings is quite challenging, largely because of the lack of…
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…