Tropical compound matrix identities

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 adj(A)det⁡(A)−1, all of which have implications on the eigenvalues of the corresponding matrices. A tropical Sylvester–Franke identit...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Linear algebra and its applications 2018-08, Vol.551, p.162-206
Hauptverfasser: Akian, Marianne, Gaubert, Stéphane, Niv, Adi
Format: Artikel
Sprache:eng
Schlagworte:
Algebra
Characteristic polynomial
Compound matrix
Definite matrices
Eigenvalues
Identity
Linear algebra
Mathematics
Matrix
Optimization and Control
Permanent
Pseudo-inverse
Rings (mathematics)
Tropical linear algebra
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Beschreibung
Zusammenfassung: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.
ISSN:0024-3795
1873-1856
DOI:10.1016/j.laa.2018.04.006