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Tropical compound matrix identities

Marianne Akian 1, 2 Stéphane Gaubert 2, 1 Adi Niv 3
2 TROPICAL - TROPICAL
CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique, Inria Saclay - Ile de France
Abstract : We 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.
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https://hal.inria.fr/hal-01469638
Contributor : Marianne Akian <>
Submitted on : Thursday, February 16, 2017 - 4:03:48 PM
Last modification on : Friday, April 30, 2021 - 10:03:51 AM

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Marianne Akian, Stéphane Gaubert, Adi Niv. Tropical compound matrix identities. Linear Algebra and its Applications, Elsevier, 2018, 551, pp.162-206. ⟨10.1016/j.laa.2018.04.006⟩. ⟨hal-01469638⟩

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