Supertropical matrix algebra

Supertropical algebra

We develop the algebraic polynomial theory for " supertropical algebra, " as initiated earlier over the real numbers by the first author. The main innovation there was the introduction of ghost elements, which play the key role in our structure theory. Here, we work in a slightly more general situation over an arbitrary semiring, and develop a theory which contains the analogs of the basic theo...

Supertropical Matrix Algebra Ii: Solving Tropical Equations Zur Izhakian and Louis Rowen

We continue the study of matrices over a supertropical algebra, proving the existence of a tangible adjoint of A, which provides the unique right (resp. left) quasi-inverse maximal with respect to the right (resp. left) quasi-identity matrix corresponding to A; this provides a unique maximal (tangible) solution to supertropical vector equations, via a version of Cramer’s rule. We also describe ...

Some results on Haar wavelets matrix through linear algebra

Can we characterize the wavelets through linear transformation? the answer for this question is certainly YES. In this paper we have characterized the Haar wavelet matrix by their linear transformation and proved some theorems on properties of Haar wavelet matrix such as Trace, eigenvalue and eigenvector and diagonalization of a matrix.

Elements of Matrix Algebra

A Glimpse at Supertropical Valuation theory

We give a short tour through major parts of a recent long paper [IKR1] on supertropical valuation theory, leaving aside nearly all proofs (to be found in [IKR1]). In this way we hope to give easy access to ideas of a new branch of so called “supertropical algebra”.