Extensors

TL;DR

This paper introduces the mathematical concept of extensors, exploring their properties, special cases, and applications, including determinants and inversion formulas, to advance the theoretical framework in this area.

Contribution

It develops the theory of extensors, defining key operators and properties, and presents initial applications demonstrating their usefulness.

Findings

Defined extension, adjoint, and generalization operators for extensors.

Established properties and formulas for determinants of (1,1)-extensors.

Provided an inversion formula for (1,1)-extensors.

Abstract

In this paper we introduce a class of mathematical objects called \emph{extensors} and develop some aspects of their theory with considerable detail. We give special names to several particular but important cases of extensors. The \emph{extension,} \emph{adjoint} and \emph{generalization} operators are introduced and their properties studied. For the so-called $(1,1)$-extensors we define the concept of \emph{determinant}, and their properties are investigated. Some preliminary applications of the theory of extensors are presented in order to show the power of the new concept in action. An useful formula for the inversion of $(1,1)$-extensors is obtained.