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Journal Articles Linear Algebra and its Applications Year : 2018

Tropical compound matrix identities


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.

Dates and versions

hal-01469638 , version 1 (16-02-2017)



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