Grassman semialgebras and the Cayley-Hamilton theorem

2018/03/21 by Letterio Gatto, Gatto, Letterio, Louis Rowen +1
Mathematics · Computer Science · #Advanced Topics in Algebra #Polynomial and algebraic computation #Matrix Theory and Algorithms

paper · pdf · doi:10.48550/arxiv.1803.08093

Abstract

We develop a theory of semialgebra Grassmann triples via Hasse-Schmidt derivations, which formally generalizes results such as the Cayley-Hamilton theorem in linear algebra, thereby providing a unified approach to classical linear algebra and tropical algebra.

Related

• Hasse--Schmidt Derivations and Cayley--Hamilton Theorem for Exterior\n Algebras
• Clifford semialgebras
• An Attempt of Construction for the Grassmann Numbers
• Remarks on the Cayley-Hamilton Theorem
• On Cachazo-Douglas-Seiberg-Witten conjecture for simple Lie algebras