On pseudo-inverses of matrices and their characteristic polynomials in supertropical algebra - Inria - Institut national de recherche en sciences et technologies du numérique Accéder directement au contenu
Article Dans Une Revue Linear Algebra and its Applications Année : 2015

On pseudo-inverses of matrices and their characteristic polynomials in supertropical algebra

Résumé

The only invertible matrices in tropical algebra are diagonal matrices, permutation matrices and their products. However, the pseudo-inverse A ∇ , defined as 1 det(A) adj(A), with det(A) being the tropical permanent (also called the tropical determinant) of a matrix A, inherits some classical algebraic properties and has some surprising new ones. Defining B and B to be tropically similar if B = A ∇ BA, we examine the characteristic (max-)polynomials of tropically similar matrices as well as those of pseudo-inverses. Other miscellaneous results include a new proof of the identity for det(AB) and a connection to stabilization of the powers of definite matrices.
Fichier principal
Vignette du fichier
nabla.pdf (408.96 Ko) Télécharger le fichier
Origine Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-01253421 , version 1 (10-01-2016)

Identifiants

Citer

Adi Niv. On pseudo-inverses of matrices and their characteristic polynomials in supertropical algebra. Linear Algebra and its Applications, 2015, 471, pp.264-290. ⟨10.1016/j.laa.2014.12.038⟩. ⟨hal-01253421⟩
151 Consultations
599 Téléchargements

Altmetric

Partager

Gmail Mastodon Facebook X LinkedIn More