2013/06/25 by Adi Niv, Niv, Adi
Computer Science · Mathematics · #13A18 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #FOS: Mathematics #Polynomial and algebraic computation #math.AC #msc:13A18
paper · pdf · doi:10.48550/arxiv.1306.5861
This paper is part of the author's PhD thesis, which was written at Bar-Ilan University under the supervision of Prof. L. H. Rowen, Journal of Linear Algebra and Applications, 2015
openalex publication_date 2013/06/25 · arxiv created 2014/12/20 · arxiv updated 2014/12/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The only invertible matrices in tropical algebra are diagonal matrices, permutation matrices and their products. However, the pseudo-inverse A^∇, defined as (adj(A))/(det(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.