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math.RA2026★ 2 cited
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…
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…