International audienceWe prove identities on compound matrices in extended tropical semirings. Such identities include analogues to properties of conjugate matrices, powers of matrices and $\operatorname{adj}(A)\det(A)^{ -1}$, all of which have implications on the eigenvalues of the corresponding matrices. A tropical Sylvester-Franke identity is provided as well
Supertropical matrix theory was investigated in [6], whose terminology we follow. In this work we in...
See also arXiv:1309.6298International audienceWe prove general Cramer type theorems for linear syste...
AbstractThe max-Łukasiewicz semiring is defined as the unit interval [0,1] equipped with the arithme...
International audienceWe prove identities on compound matrices in extended tropical semirings. Such ...
13 pagesWe prove the conjecture that, for any $n$, the monoid of all $n \times n$ tropical matrices ...
International audienceThe only invertible matrices in tropical algebra are diagonal matrices, permut...
The tropical semiring is ℝ ∪ {∞} with the operations x ⊕ y = min{x, y}, x ⊕ ∞ = ∞ ⊕ x = x, x ⊙ y = x...
Tropical linear algebra is the study of classical linear algebra problems with arithmetic done over ...
We establish necessary and sufficient conditions for a semigroup identity to hold in the monoid of n...
arXiv:1606.00238International audienceWe investigate the tropical analogues of totally positive and ...
structure of the semigroup of n × n tropical matrices and its connection with the geometry of tropic...
AbstractWe study the algebraic structure of the semigroup of all 2×2 tropical matrices under multipl...
We study the algebraic structure of the semigroup of all 2 2 tropical matrices under multiplication...
AbstractWe study Green’s J-order and J-equivalence for the semigroup of all n×n matrices over the tr...
Abstract. Supertropical matrix theory was investigated in [6], whose terminology we follow. In this ...
Supertropical matrix theory was investigated in [6], whose terminology we follow. In this work we in...
See also arXiv:1309.6298International audienceWe prove general Cramer type theorems for linear syste...
AbstractThe max-Łukasiewicz semiring is defined as the unit interval [0,1] equipped with the arithme...
International audienceWe prove identities on compound matrices in extended tropical semirings. Such ...
13 pagesWe prove the conjecture that, for any $n$, the monoid of all $n \times n$ tropical matrices ...
International audienceThe only invertible matrices in tropical algebra are diagonal matrices, permut...
The tropical semiring is ℝ ∪ {∞} with the operations x ⊕ y = min{x, y}, x ⊕ ∞ = ∞ ⊕ x = x, x ⊙ y = x...
Tropical linear algebra is the study of classical linear algebra problems with arithmetic done over ...
We establish necessary and sufficient conditions for a semigroup identity to hold in the monoid of n...
arXiv:1606.00238International audienceWe investigate the tropical analogues of totally positive and ...
structure of the semigroup of n × n tropical matrices and its connection with the geometry of tropic...
AbstractWe study the algebraic structure of the semigroup of all 2×2 tropical matrices under multipl...
We study the algebraic structure of the semigroup of all 2 2 tropical matrices under multiplication...
AbstractWe study Green’s J-order and J-equivalence for the semigroup of all n×n matrices over the tr...
Abstract. Supertropical matrix theory was investigated in [6], whose terminology we follow. In this ...
Supertropical matrix theory was investigated in [6], whose terminology we follow. In this work we in...
See also arXiv:1309.6298International audienceWe prove general Cramer type theorems for linear syste...
AbstractThe max-Łukasiewicz semiring is defined as the unit interval [0,1] equipped with the arithme...
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