Tropical compound matrix identities

Marianne Akian; Stéphane Gaubert; Adi Niv

doi:10.1016/j.laa.2018.04.006

Tropical compound matrix identities

Mathematics Department

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Résumé

We prove identities on compound matrices in extended tropical semirings. Such identities include analogues to properties of conjugate matrices, powers of matrices and 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.

langue originale	Anglais
Pages (de - à)	162-206
Nombre de pages	45
journal	Linear Algebra and Its Applications
Volume	551
Les DOIs	https://doi.org/10.1016/j.laa.2018.04.006
état	Publié - 15 août 2018

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10.1016/j.laa.2018.04.006

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title = "Tropical compound matrix identities",

abstract = "We prove identities on compound matrices in extended tropical semirings. Such identities include analogues to properties of conjugate matrices, powers of matrices and 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.",

keywords = "Characteristic polynomial, Compound matrix, Definite matrices, Eigenvalues, Permanent, Pseudo-inverse, Tropical linear algebra",

author = "Marianne Akian and St{\'e}phane Gaubert and Adi Niv",

note = "Publisher Copyright: {\textcopyright} 2018 Elsevier Inc.",

year = "2018",

month = aug,

day = "15",

doi = "10.1016/j.laa.2018.04.006",

language = "English",

volume = "551",

pages = "162--206",

journal = "Linear Algebra and Its Applications",

issn = "0024-3795",

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TY - JOUR

T1 - Tropical compound matrix identities

AU - Akian, Marianne

AU - Gaubert, Stéphane

AU - Niv, Adi

PY - 2018/8/15

Y1 - 2018/8/15

N2 - We prove identities on compound matrices in extended tropical semirings. Such identities include analogues to properties of conjugate matrices, powers of matrices and 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.

AB - We prove identities on compound matrices in extended tropical semirings. Such identities include analogues to properties of conjugate matrices, powers of matrices and 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.

KW - Characteristic polynomial

KW - Compound matrix

KW - Definite matrices

KW - Eigenvalues

KW - Permanent

KW - Pseudo-inverse

KW - Tropical linear algebra

UR - https://www.scopus.com/pages/publications/85045466463

U2 - 10.1016/j.laa.2018.04.006

DO - 10.1016/j.laa.2018.04.006

M3 - Article

AN - SCOPUS:85045466463

SN - 0024-3795

VL - 551

SP - 162

EP - 206

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

ER -

Tropical compound matrix identities

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